Application of derivatives Questions and Answers
![Use technology to find points and then graph the function y 2log 2 8 1 following the instructions below done plotting points Plot at least five points with integer coordinates that fit on the axes below Click a point to delete it](https://media.kunduz.com/media/sug-question-candidate/20231018212831106981-6097020.jpg?w=256)
Calculus
Application of derivativesUse technology to find points and then graph the function y 2log 2 8 1 following the instructions below done plotting points Plot at least five points with integer coordinates that fit on the axes below Click a point to delete it
![2 Determine the absolute extrema of the function on the closed interval given K f x 4x x 1 where x 0 4](https://media.kunduz.com/media/sug-question-candidate/20231018201655680139-4754400.jpg?w=256)
Calculus
Application of derivatives2 Determine the absolute extrema of the function on the closed interval given K f x 4x x 1 where x 0 4
![8 A boat leaves a dock at 2 00 pm heading west at 15 km h Another boat heads south at 12 km h and reaches the same dock at 3 00 pm At what time were the boats closest to each other Round to 2 decimal places Interval not needed](https://media.kunduz.com/media/sug-question-candidate/20231018183048851848-4754400.jpg?w=256)
Calculus
Application of derivatives8 A boat leaves a dock at 2 00 pm heading west at 15 km h Another boat heads south at 12 km h and reaches the same dock at 3 00 pm At what time were the boats closest to each other Round to 2 decimal places Interval not needed
![4 1 Determine the absolute maximum and minimum values for the function below on the given interval K 1 5 S x x x 6x where 0 x 4 3 2 Minimum Value at x](https://media.kunduz.com/media/sug-question-candidate/20231018182712371347-4754400.jpg?w=256)
Calculus
Application of derivatives4 1 Determine the absolute maximum and minimum values for the function below on the given interval K 1 5 S x x x 6x where 0 x 4 3 2 Minimum Value at x
![Determine the absolute extrema of the function on the closed interval given K f x 4x x 1 where x 0 4](https://media.kunduz.com/media/sug-question-candidate/20231018182730132762-4754400.jpg?w=256)
Calculus
Application of derivativesDetermine the absolute extrema of the function on the closed interval given K f x 4x x 1 where x 0 4
![2 7 Finding where the derivative of a function equals zero will always produce the desired optimal value Is this statement true or false Explain your reasoning C](https://media.kunduz.com/media/sug-question-candidate/20231018183031893950-4754400.jpg?w=256)
Calculus
Application of derivatives2 7 Finding where the derivative of a function equals zero will always produce the desired optimal value Is this statement true or false Explain your reasoning C
![6 Explain why we cannot determine maximum or minimum values for the function f x X x 3 interval 5 x 5 Include in a sketch in your solution C over the](https://media.kunduz.com/media/sug-question-candidate/20231018183015997320-4754400.jpg?w=256)
Calculus
Application of derivatives6 Explain why we cannot determine maximum or minimum values for the function f x X x 3 interval 5 x 5 Include in a sketch in your solution C over the
![5 A cylindrical tank with no top is to be built from stainless steel with a copper bottom The tank is to have a volume of 5 m If the price of copper is five times the price of stainless steel what should be the dimensions of the tank so that the cost is a minimum Interval not needed A Vcylinder h SACylinder 2tr 2 rh](https://media.kunduz.com/media/sug-question-candidate/20231018182906294846-4754400.jpg?w=256)
Calculus
Application of derivatives5 A cylindrical tank with no top is to be built from stainless steel with a copper bottom The tank is to have a volume of 5 m If the price of copper is five times the price of stainless steel what should be the dimensions of the tank so that the cost is a minimum Interval not needed A Vcylinder h SACylinder 2tr 2 rh
![nalyze the polynomial function f x x x 5 using parts a through h below Determine the end behavior of the graph of the function he graph of f behaves like y for large values of x](https://media.kunduz.com/media/sug-question-candidate/20231018161420261108-5472891.jpg?w=256)
Calculus
Application of derivativesnalyze the polynomial function f x x x 5 using parts a through h below Determine the end behavior of the graph of the function he graph of f behaves like y for large values of x
![Hiring nilai us X 2x J 1 x](https://media.kunduz.com/media/sug-question-candidate/20231018101307649792-5367663.jpg?w=256)
![4 Points DETAILS SPRECALC7COREQ 3 5 001 The polynomial P x 5x x 2 x 8 has degree It has zeros 0 2 and The zero 0 has multiplicity and the zero 2 has multiplicity](https://media.kunduz.com/media/sug-question-candidate/20231018055157675235-3865561.jpg?w=256)
Calculus
Application of derivatives4 Points DETAILS SPRECALC7COREQ 3 5 001 The polynomial P x 5x x 2 x 8 has degree It has zeros 0 2 and The zero 0 has multiplicity and the zero 2 has multiplicity
![Given the graph of f x below find the graph of the derivative of f x Select the correct answer below 6 5 4 3 2 SH Y N 3 4 5 6](https://media.kunduz.com/media/sug-question-candidate/20231018032142648101-5957113.jpg?w=256)
Calculus
Application of derivativesGiven the graph of f x below find the graph of the derivative of f x Select the correct answer below 6 5 4 3 2 SH Y N 3 4 5 6
![Find the open interval s of f x graph given below where f x is negative 6 Provide your answer below S 43 4 3 2 6 5 4 3 2 1 1 2 3 4 5 6 5 6 Give your answer in interval notation For example 2 4 U 6 00 141](https://media.kunduz.com/media/sug-question-candidate/20231018025301635838-5957113.jpg?w=256)
Calculus
Application of derivativesFind the open interval s of f x graph given below where f x is negative 6 Provide your answer below S 43 4 3 2 6 5 4 3 2 1 1 2 3 4 5 6 5 6 Give your answer in interval notation For example 2 4 U 6 00 141
![5 and p Construct a Binomial probability distrubtion table using n 0 24 Next record the mean am standard deviation of the distribution below Where necessary round all numbers to four decimal places x P x](https://media.kunduz.com/media/sug-question-candidate/20231018022514457124-3618741.jpg?w=256)
Calculus
Application of derivatives5 and p Construct a Binomial probability distrubtion table using n 0 24 Next record the mean am standard deviation of the distribution below Where necessary round all numbers to four decimal places x P x
![57 60 Use a graphing device to graph the polar curve Choose the parameter interval to make sure that you produce the entire curve STUT 0 57 r esin 2 cos 40 butterfly curve](https://media.kunduz.com/media/sug-question-candidate/20231018020840422094-5865088.jpg?w=256)
Calculus
Application of derivatives57 60 Use a graphing device to graph the polar curve Choose the parameter interval to make sure that you produce the entire curve STUT 0 57 r esin 2 cos 40 butterfly curve
![2 Consider the series n 1 n 2 n 1 a x Use your computer to graph the functions f x 32 and g x 3 2 on the same set of axes You can use Desmos or your graphing calculator Set the scale on the horizontal axis so the x values go from 1 to 100 We are interested in comparing the functions for large values of x and when x is large both f x and g x are quite small Thus you should set the scale on the vertical axis to view the y values between 0 and 1 If you are using Desmos use the wrench button at the top right of your screen to set the vertical scale b Now use your computer to plot the function f x from part a together with h x You may have to experiment to find a range of y values that will enable you to see both functions on the same axes f x f x limx and limx h for the functions in parts a and b c Calculate above You can do this by hand or use the graphs of the quotients on desmos and see what happens as x goes to You don t have to show your work here but what are the limits d Look at the results of parts a through c and the statement of the LCT Should 1 you compare the series En 1 n 2 7 with n 1 7 2 or with n 1 Explain your choice after considering which term dominates the denominator for large values of n n 1n n e Does the series n 1 n 2 n converge Use the LCT and your knowledge of p series to justify your conclusion](https://media.kunduz.com/media/sug-question-candidate/20231018013214133939-5870859.jpg?w=256)
Calculus
Application of derivatives2 Consider the series n 1 n 2 n 1 a x Use your computer to graph the functions f x 32 and g x 3 2 on the same set of axes You can use Desmos or your graphing calculator Set the scale on the horizontal axis so the x values go from 1 to 100 We are interested in comparing the functions for large values of x and when x is large both f x and g x are quite small Thus you should set the scale on the vertical axis to view the y values between 0 and 1 If you are using Desmos use the wrench button at the top right of your screen to set the vertical scale b Now use your computer to plot the function f x from part a together with h x You may have to experiment to find a range of y values that will enable you to see both functions on the same axes f x f x limx and limx h for the functions in parts a and b c Calculate above You can do this by hand or use the graphs of the quotients on desmos and see what happens as x goes to You don t have to show your work here but what are the limits d Look at the results of parts a through c and the statement of the LCT Should 1 you compare the series En 1 n 2 7 with n 1 7 2 or with n 1 Explain your choice after considering which term dominates the denominator for large values of n n 1n n e Does the series n 1 n 2 n converge Use the LCT and your knowledge of p series to justify your conclusion
![Given the graph of f x below what is the open interval s over which f x is positive 6 5 4 3 H 1 2 3 4 5 6](https://media.kunduz.com/media/sug-question-candidate/20231018015908354955-5957113.jpg?w=256)
Calculus
Application of derivativesGiven the graph of f x below what is the open interval s over which f x is positive 6 5 4 3 H 1 2 3 4 5 6
![Given the graph of f x below identify the graph of f x 6 5 4 3 2 1 6 5 4 3 1 2 3 4 31 H 1 2 3 4 5 6](https://media.kunduz.com/media/sug-question-candidate/20231018013946397359-5957113.jpg?w=256)
Calculus
Application of derivativesGiven the graph of f x below identify the graph of f x 6 5 4 3 2 1 6 5 4 3 1 2 3 4 31 H 1 2 3 4 5 6
![question You can retry this question below A large company determines that in t months the number of units in the thousands that they will have 11t 3 produced is given by p t t 4 dollars Question Help Message instructor What will happen to the production in the long run](https://media.kunduz.com/media/sug-question-candidate/20231017234015500603-5868017.jpg?w=256)
Calculus
Application of derivativesquestion You can retry this question below A large company determines that in t months the number of units in the thousands that they will have 11t 3 produced is given by p t t 4 dollars Question Help Message instructor What will happen to the production in the long run
![Evaluate the limit lim 3 tan 4x Enter a simplified multiple of or or x48](https://media.kunduz.com/media/sug-question-candidate/20231017233945165733-5868017.jpg?w=256)
Calculus
Application of derivativesEvaluate the limit lim 3 tan 4x Enter a simplified multiple of or or x48
![Question 12 Evaluate lim sin 9x o A](https://media.kunduz.com/media/sug-question-candidate/20231017233915244869-5868017.jpg?w=256)
![Evaluate the limit using L H pital s rule 7x lim X18 e5x](https://media.kunduz.com/media/sug-question-candidate/20231017233751336238-5868017.jpg?w=256)
![Question 4 lim x 0 Evaluate the limit using L Hospital s rule 4 5 X](https://media.kunduz.com/media/sug-question-candidate/20231017233726653471-5868017.jpg?w=256)
Calculus
Application of derivativesQuestion 4 lim x 0 Evaluate the limit using L Hospital s rule 4 5 X
![The lesser til is a zentiplicity so the graph on OA o OA d Use a graphing utility to graph the function The graphs are shown in the viewing window Xmin B pants a through n Classes B Ay 1600 IOW e Approximate the turning points of the graph The turning point s of the graph is are 1 25 759 69 Type an ordered pair Round each coordinate to the nearest hundredth as needed Use a comma to separate answers as needed f Use the information in parts a through e to draw a complete graph of the function by hand Choose the correct graph below S X The gitaiti i is a ti miplicity the graph in Crosses f A axis al x 4 10 Xmax 10 Xscl 1 Ymin 1600 Yn 1600 Y 160 Choose the correct graph below max O C C 1 1600 O D D 57 Q](https://media.kunduz.com/media/sug-question-candidate/20231017223243527862-5472891.jpg?w=256)
Calculus
Application of derivativesThe lesser til is a zentiplicity so the graph on OA o OA d Use a graphing utility to graph the function The graphs are shown in the viewing window Xmin B pants a through n Classes B Ay 1600 IOW e Approximate the turning points of the graph The turning point s of the graph is are 1 25 759 69 Type an ordered pair Round each coordinate to the nearest hundredth as needed Use a comma to separate answers as needed f Use the information in parts a through e to draw a complete graph of the function by hand Choose the correct graph below S X The gitaiti i is a ti miplicity the graph in Crosses f A axis al x 4 10 Xmax 10 Xscl 1 Ymin 1600 Yn 1600 Y 160 Choose the correct graph below max O C C 1 1600 O D D 57 Q
![e Approximate the turning points of the graph The turning point s of the graph is are 3 16 34 33 5 16 6 90 Type an ordered pair Round each coordinate to the nearest hundredth as needed Use a comma to separate answers as needed f Use the information in parts a through e to draw a complete graph of the function by hand Choose the correct graph below OA wer parts a through h B Ay g From the graph find the range of the polynomial function The range of the polynomial function f is 0 00 Type your answer in interval notation Round to the nearest hundredth as needed h Use the graph to determine where the function is increasing and where it is decreasing The function is increasing on the interval s pooded Use a comma to separate answers as needed D](https://media.kunduz.com/media/sug-question-candidate/20231017215929827718-5472891.jpg?w=256)
Calculus
Application of derivativese Approximate the turning points of the graph The turning point s of the graph is are 3 16 34 33 5 16 6 90 Type an ordered pair Round each coordinate to the nearest hundredth as needed Use a comma to separate answers as needed f Use the information in parts a through e to draw a complete graph of the function by hand Choose the correct graph below OA wer parts a through h B Ay g From the graph find the range of the polynomial function The range of the polynomial function f is 0 00 Type your answer in interval notation Round to the nearest hundredth as needed h Use the graph to determine where the function is increasing and where it is decreasing The function is increasing on the interval s pooded Use a comma to separate answers as needed D
![3 If the price charged for a candy bar is p x cents then x thousand candy bars will be sold in a certain city where p x 149 2 How many candy bars must be sold to maximize revenue A 1937 thousand candy bars C 1937 candy bars B 3874 candy bars D 3874 thousand candy bars](https://media.kunduz.com/media/sug-question-candidate/20231017213357197559-6051355.jpg?w=256)
Calculus
Application of derivatives3 If the price charged for a candy bar is p x cents then x thousand candy bars will be sold in a certain city where p x 149 2 How many candy bars must be sold to maximize revenue A 1937 thousand candy bars C 1937 candy bars B 3874 candy bars D 3874 thousand candy bars
![Analyze the polynomial function f x 3 x 3 x 4 using parts a through h below The graph of f behaves like y 3x for large values of x b Find the x and y intercepts of the graph of the function The x intercept s is are 3 4 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once The y intercept s is are 576 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once c Determine the real zeros of the function and their multiplicity Use this information to determine whether the graph crosses or touches the x axis at each x intercept The real zero s of f is are 3 4 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once Y min 1600 Y max The lesser zero is a zero of multiplicity 1 so the graph of f crosses the x axis at X 3 The greater zero is a zero of multiplicity 3 so the graph of f crosses the x axis at x 4 d Use a graphing utility to graph the function The graphs are shown in the viewing window Xmin 10 Xmax 10 Xscl 1 1600 Yscl 160 Choose the correct graph below OA www C B O C OU O D](https://media.kunduz.com/media/sug-question-candidate/20231017212954700613-5472891.jpg?w=256)
Calculus
Application of derivativesAnalyze the polynomial function f x 3 x 3 x 4 using parts a through h below The graph of f behaves like y 3x for large values of x b Find the x and y intercepts of the graph of the function The x intercept s is are 3 4 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once The y intercept s is are 576 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once c Determine the real zeros of the function and their multiplicity Use this information to determine whether the graph crosses or touches the x axis at each x intercept The real zero s of f is are 3 4 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once Y min 1600 Y max The lesser zero is a zero of multiplicity 1 so the graph of f crosses the x axis at X 3 The greater zero is a zero of multiplicity 3 so the graph of f crosses the x axis at x 4 d Use a graphing utility to graph the function The graphs are shown in the viewing window Xmin 10 Xmax 10 Xscl 1 1600 Yscl 160 Choose the correct graph below OA www C B O C OU O D
![ind the general form of the quadratic function with the vertex 3 2 and a point on the graph 5 6 f x help formulas](https://media.kunduz.com/media/sug-question-candidate/20231017202137329409-4704102.jpg?w=256)
Calculus
Application of derivativesind the general form of the quadratic function with the vertex 3 2 and a point on the graph 5 6 f x help formulas
![Find the general form of the quadratic function that has a vertex of 2 2 and a point on the graph 5 51 f x help formulas](https://media.kunduz.com/media/sug-question-candidate/20231017202113522968-4704102.jpg?w=256)
Calculus
Application of derivativesFind the general form of the quadratic function that has a vertex of 2 2 and a point on the graph 5 51 f x help formulas
![Rewrite the quadratic function f x x 8x 3 in standard form f x a x h k and give the vertex help numbers f x Vertex Ex Quadratic Function Reviewerview Use f x 2x 45x 3 for the following questions f x ax bx 1 Does the parabola open up or down The parabola opens down 2 Determine the equation of the axis of symmetry b X 2a the vertex Xa 3 Determine the co H Q x 4 Determine the x and y intercepts x ints set f x 0 y int set ka0 2 0 3 0 help points 6 2 8 S 2 0 2x 5x 3 0 27 5x 3 OF 2x 12x 3 2x 1 0 or X 3 0 x 3 G](https://media.kunduz.com/media/sug-question-candidate/20231017201845386088-4704102.jpg?w=256)
Calculus
Application of derivativesRewrite the quadratic function f x x 8x 3 in standard form f x a x h k and give the vertex help numbers f x Vertex Ex Quadratic Function Reviewerview Use f x 2x 45x 3 for the following questions f x ax bx 1 Does the parabola open up or down The parabola opens down 2 Determine the equation of the axis of symmetry b X 2a the vertex Xa 3 Determine the co H Q x 4 Determine the x and y intercepts x ints set f x 0 y int set ka0 2 0 3 0 help points 6 2 8 S 2 0 2x 5x 3 0 27 5x 3 OF 2x 12x 3 2x 1 0 or X 3 0 x 3 G
![For the quadratic function f x x 4x 5 find the vertex the axis of symmetry and the x intercept s Express the vertex as a coordinate pair If there is more than one intercept enter as a comma separated list of points help points vertex axis of symmetry x intercept s help numbers help points](https://media.kunduz.com/media/sug-question-candidate/20231017202156385094-4704102.jpg?w=256)
Calculus
Application of derivativesFor the quadratic function f x x 4x 5 find the vertex the axis of symmetry and the x intercept s Express the vertex as a coordinate pair If there is more than one intercept enter as a comma separated list of points help points vertex axis of symmetry x intercept s help numbers help points
![Determine whether f x 4x 16x 4 has a minimum or maximum value and find the value of the minimum or maximum Also find the axis of symmetry The y value of the is The axis of symmetry for f x is given by help numbers help numbers](https://media.kunduz.com/media/sug-question-candidate/20231017202015207002-4704102.jpg?w=256)
Calculus
Application of derivativesDetermine whether f x 4x 16x 4 has a minimum or maximum value and find the value of the minimum or maximum Also find the axis of symmetry The y value of the is The axis of symmetry for f x is given by help numbers help numbers
![Determine the domain and range of f x 7 x 5 3 Enter the solution in interval notation help intervals Domain Range help intervals](https://media.kunduz.com/media/sug-question-candidate/20231017202045035391-4704102.jpg?w=256)
Calculus
Application of derivativesDetermine the domain and range of f x 7 x 5 3 Enter the solution in interval notation help intervals Domain Range help intervals
![C f x x 0 16 Graph the function the secant line through the endpoints and the tangent line at c f c y y 5 15 10 5 y 15 10 1 2 3 5 3 5 10 15 1 separated list If an answer does not exist enter DNE](https://media.kunduz.com/media/sug-question-candidate/20231017182111693680-5886119.jpg?w=256)
Calculus
Application of derivativesC f x x 0 16 Graph the function the secant line through the endpoints and the tangent line at c f c y y 5 15 10 5 y 15 10 1 2 3 5 3 5 10 15 1 separated list If an answer does not exist enter DNE
![13 3 Analyze the polynomial function f x x x 7x 21 Answer parts a through h 24 8 8 3 4 8 8 e Approximate the turning points of the graph The turning point s of the graph is are 3 16 34 33 5 16 6 90 Type an ordered pair Round each coordinate to the nearest hundredth as needed Use a comma to separate answers as needed f Use the information in parts a through e to draw a complete graph of the function by hand Choose the correct graph below OA www B 100 Ay O C O D](https://media.kunduz.com/media/sug-question-candidate/20231017185447753568-5472891.jpg?w=256)
Calculus
Application of derivatives13 3 Analyze the polynomial function f x x x 7x 21 Answer parts a through h 24 8 8 3 4 8 8 e Approximate the turning points of the graph The turning point s of the graph is are 3 16 34 33 5 16 6 90 Type an ordered pair Round each coordinate to the nearest hundredth as needed Use a comma to separate answers as needed f Use the information in parts a through e to draw a complete graph of the function by hand Choose the correct graph below OA www B 100 Ay O C O D
![For the polynomial function f x 8x x 2 answer the following questions a List each real zero and its multiplicity b Determine whether the graph crosses or touches the x axis at each x intercept c Determine the maximum number of turning points on the graph d Determine the end behavior that is find the power function that the graph of f resembles for large values of x b Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The graph crosses the x axis at Type an exact answer using radicals as needed Type an integer or a simplified fraction Use a comma to separate answers as needed OB The graph touches the x axis at Type an exact answer using radicals as needed Type an integer or a simplified fraction Use a comma to separate answers as needed C The graph touches the x axis at 0 and crosses at 2 2 Type integers or simplified fractions Use a comma to separate answers as needed OD The graph neither crosses nor touches the x axis c The maximum number of turning points on the graph is Tyng a whole number](https://media.kunduz.com/media/sug-question-candidate/20231017183303837241-5472891.jpg?w=256)
Calculus
Application of derivativesFor the polynomial function f x 8x x 2 answer the following questions a List each real zero and its multiplicity b Determine whether the graph crosses or touches the x axis at each x intercept c Determine the maximum number of turning points on the graph d Determine the end behavior that is find the power function that the graph of f resembles for large values of x b Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The graph crosses the x axis at Type an exact answer using radicals as needed Type an integer or a simplified fraction Use a comma to separate answers as needed OB The graph touches the x axis at Type an exact answer using radicals as needed Type an integer or a simplified fraction Use a comma to separate answers as needed C The graph touches the x axis at 0 and crosses at 2 2 Type integers or simplified fractions Use a comma to separate answers as needed OD The graph neither crosses nor touches the x axis c The maximum number of turning points on the graph is Tyng a whole number
![8 A town with a population of 100 people grows to a population of 200 in five years Assume the dP population P grows exponentially according to the equation kP Find the relative growth rate dt k](https://media.kunduz.com/media/sug-question-candidate/20231017180712315746-5886119.jpg?w=256)
Calculus
Application of derivatives8 A town with a population of 100 people grows to a population of 200 in five years Assume the dP population P grows exponentially according to the equation kP Find the relative growth rate dt k
![2 Compute the derivative for the function y x e dy dx Note you do not need to simplify your answer](https://media.kunduz.com/media/sug-question-candidate/20231017180546524763-5886119.jpg?w=256)
Calculus
Application of derivatives2 Compute the derivative for the function y x e dy dx Note you do not need to simplify your answer
![5 When 2x xy 4y 2 express dy in terms of x and y using implicit differentiation dx](https://media.kunduz.com/media/sug-question-candidate/20231017180627098356-5886119.jpg?w=256)
Calculus
Application of derivatives5 When 2x xy 4y 2 express dy in terms of x and y using implicit differentiation dx
![Analyze the polynomial function The y intercept s is are 21 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once c Determine the zeros of the function and their multiplicity Use this information to determine whether the graph crosses or touches the x axis at each x intercept The real zero s of f is are 7 3 7 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once A Answer parts a through h The least zero is of multiplicity 1 so the graph of f crosses the x axis at x graph off crosses the x axis at x 7 d Use a graphing utility to graph the function The graphs are shown in the viewing window Xmin 5 B 7 The middle zero is of multiplicity 1 so the graph of f crosses the x axis at x 3 The greatest zero is of mult 10 Xmax 10 Xscl 1 Ymin 50 Ymax 50 Y sci 5 Choose the correct graph below O C Q O D o O 5](https://media.kunduz.com/media/sug-question-candidate/20231017172927024152-5472891.jpg?w=256)
Calculus
Application of derivativesAnalyze the polynomial function The y intercept s is are 21 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once c Determine the zeros of the function and their multiplicity Use this information to determine whether the graph crosses or touches the x axis at each x intercept The real zero s of f is are 7 3 7 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once A Answer parts a through h The least zero is of multiplicity 1 so the graph of f crosses the x axis at x graph off crosses the x axis at x 7 d Use a graphing utility to graph the function The graphs are shown in the viewing window Xmin 5 B 7 The middle zero is of multiplicity 1 so the graph of f crosses the x axis at x 3 The greatest zero is of mult 10 Xmax 10 Xscl 1 Ymin 50 Ymax 50 Y sci 5 Choose the correct graph below O C Q O D o O 5
![The radius of a sphere is increasing at a rate of 3 mm s How fast is the volume increasing when the diameter is 80 mm mm s](https://media.kunduz.com/media/sug-question-candidate/20231017150712176178-5886119.jpg?w=256)
Calculus
Application of derivativesThe radius of a sphere is increasing at a rate of 3 mm s How fast is the volume increasing when the diameter is 80 mm mm s
![R If two resistors with resistances R and R are connected in parallel as in the figure below then the total resistance R measured in ohms 22 is given by 1 1 2 22 R If R and R are increasing at rates of 0 3 2 s and 0 2 2 s respectively how fast is R changing when R 100 2 and R 110 2 Round your answer to three decimal places 22 s www MY NOTES R PRACTIC](https://media.kunduz.com/media/sug-question-candidate/20231017150822357467-5886119.jpg?w=256)
Calculus
Application of derivativesR If two resistors with resistances R and R are connected in parallel as in the figure below then the total resistance R measured in ohms 22 is given by 1 1 2 22 R If R and R are increasing at rates of 0 3 2 s and 0 2 2 s respectively how fast is R changing when R 100 2 and R 110 2 Round your answer to three decimal places 22 s www MY NOTES R PRACTIC
![h x 2x 15x 144x 1 Given the function above use the First Derivative Test to find the local extrema Select the correct answer below There is a local maximum at x 8 O There is a local maximum at x 3 O There is a local minimum at x 8 and a local maximum at x 3 There is a local maximum at x 8 and a local minimum at x 3 There is a local minimum at x 3](https://media.kunduz.com/media/sug-question-candidate/20231017144150824193-5957113.jpg?w=256)
Calculus
Application of derivativesh x 2x 15x 144x 1 Given the function above use the First Derivative Test to find the local extrema Select the correct answer below There is a local maximum at x 8 O There is a local maximum at x 3 O There is a local minimum at x 8 and a local maximum at x 3 There is a local maximum at x 8 and a local minimum at x 3 There is a local minimum at x 3
![The line y 5 is a horizontal asymptote to the graph of which of the following functi sin 5x y B y 5x C y 5x D 1 x 1 x 5 E y 20x 1 4x](https://media.kunduz.com/media/sug-question-candidate/20231017135601101535-6122537.jpg?w=256)
Calculus
Application of derivativesThe line y 5 is a horizontal asymptote to the graph of which of the following functi sin 5x y B y 5x C y 5x D 1 x 1 x 5 E y 20x 1 4x
![Graph of 18 The graph of a function is shown above Which of the following limits does not exist E lim f x A lim f x B im f x C lim f x D lim f x 19 Let be the function defined by f x 3x 8 5 4x Which of the following is a horizontal asymptote to 2x 1 2 the graph of f A y 6 B y 3 0 y 12 2 D y 0 E y 2](https://media.kunduz.com/media/sug-question-candidate/20231017122709664693-6122145.jpg?w=256)
Calculus
Application of derivativesGraph of 18 The graph of a function is shown above Which of the following limits does not exist E lim f x A lim f x B im f x C lim f x D lim f x 19 Let be the function defined by f x 3x 8 5 4x Which of the following is a horizontal asymptote to 2x 1 2 the graph of f A y 6 B y 3 0 y 12 2 D y 0 E y 2
![B 2 16 C 3 D nonexistent If f is a continuous function such that f 2 6 which of the following statements must be A lim 2x 3 B lim 2x 12 f x f 2 6 C lim D lim x 36 E lim f x 36 7 For which of the following pairs of functions f and g is lim 818 A f x x 2x and g x x ln x B f x 3x and g x x C f x 3 and g x x D f x 3e x and g x E f x In 3x and g x In 2x and g x 2e x f x infinite g x](https://media.kunduz.com/media/sug-question-candidate/20231017122509460288-6122145.jpg?w=256)
Calculus
Application of derivativesB 2 16 C 3 D nonexistent If f is a continuous function such that f 2 6 which of the following statements must be A lim 2x 3 B lim 2x 12 f x f 2 6 C lim D lim x 36 E lim f x 36 7 For which of the following pairs of functions f and g is lim 818 A f x x 2x and g x x ln x B f x 3x and g x x C f x 3 and g x x D f x 3e x and g x E f x In 3x and g x In 2x and g x 2e x f x infinite g x
![1 Is the function f x continuous at x 27 Give a reason for your answer t hrs v t miy hr 1 2 4 5 7 3 8 6 10 3 2 A bug walks back and forth along a straight track The bug s velocity measured in miles per hour i ontinuous with selected values of the velocity shown in the table above time for 4 7 such that the velocity of the bug equals 0 Explain your reasoning](https://media.kunduz.com/media/sug-question-candidate/20231017103823438977-6011704.jpg?w=256)
Calculus
Application of derivatives1 Is the function f x continuous at x 27 Give a reason for your answer t hrs v t miy hr 1 2 4 5 7 3 8 6 10 3 2 A bug walks back and forth along a straight track The bug s velocity measured in miles per hour i ontinuous with selected values of the velocity shown in the table above time for 4 7 such that the velocity of the bug equals 0 Explain your reasoning
![et x 0 Find y using implicit differentiation if xy y 1 0](https://media.kunduz.com/media/sug-question-candidate/20231017104001679747-6116568.jpg?w=256)
![Here is the graph of a quadratic function f 5 0 12 10 5 0 2 0 5 4 4 Of x x 4 4 5 6 0 Select all equations that could define the function f Of x x 4 4 Of x x 8x 12 Of x x 2 x 6 Of x x 2 x 6 f x x 8x 12 10](https://media.kunduz.com/media/sug-question-candidate/20231017094214373387-6060199.jpg?w=256)
Calculus
Application of derivativesHere is the graph of a quadratic function f 5 0 12 10 5 0 2 0 5 4 4 Of x x 4 4 5 6 0 Select all equations that could define the function f Of x x 4 4 Of x x 8x 12 Of x x 2 x 6 Of x x 2 x 6 f x x 8x 12 10
![Prove the identity tan x 1 tan x 3 1 3 tan x 1 3 tan x tan x tan F 3 tan x 3 1 3 tan x 3 tan x 1 3 tan x X](https://media.kunduz.com/media/sug-question-candidate/20231017033645942414-4729556.jpg?w=256)
Calculus
Application of derivativesProve the identity tan x 1 tan x 3 1 3 tan x 1 3 tan x tan x tan F 3 tan x 3 1 3 tan x 3 tan x 1 3 tan x X