Application of derivatives Questions and Answers

The series True False 1 ne n 0 converges when p 2 1

Evaluate the integral U 2 3 6x dx 21 4

Question Find the roots of f x x 7x 10x and their multiplicities has a multiplicity of The root Select Select Select The root Select Select Select The root Select Select Select which means the graph the x axis at that point has a multiplicity of which means the graph the x axis at that point has a multiplicity of which means the graph the x axis at that point

Question How is the graph of 2f 4x 1 7 different from the graph of f x In other words what do the numbers 2 4 1 and 7 tell us The 2 is a Select The 2 makes the graph Select tells us to Select The 4 is Select The 4 makes the graph Select tells us to Select The 1 is a Select The 1 makes the graph Select tells us to Select The 7 is a Select The 7 makes the graph Select Select Select Select Select and the negative sign and the negative sign and the positive sign and the positive sign

A person s height depends on their age 1 This situation describes a function y f x where the two variables are the person s age in years and the person s height in inches Which variable is age and which variable is height X Select and y Select 2 What would you expect the range of the function to be if Dom f 0 85 Ran f

A company is considering a new manufacturing process It knows that the rate of savings in dollars per year from the process will be about S t 1000 t 4 where t is the number of years the process has been in use Find the total savings during the first year Find the total savings during the first 7 years The total savings during the first year is Simplify your answer The total savings during the first 7 years is Simplify your answer

below A person s height depends on their age This situation describes a function where the two variables are the person s age in years and the person s height in inches Which variable is age and which variable is height and What would you expect the range of the function to be if Where would you expect the function to be increasing and decreasing The function should be increasing from about x to about x The function should be decreasing from about x to about x Which of the images below could be a graph of f x f x Graph starts at a 0 increases to 70 inches at 18 yrs stays the same until declining slightly before age 85 g x A straight line graph starting at zero that increases equally over time until it reaches 70 inches at 85 years h x Hyperbola starts at 0 increases to 70 in at 40 yrs declines until it returns to original height at 85 What would the y intercept of the function tell you in terms of age and height Would you expect such a point to exist The y intercept tells us I expect such a point to exist because What would the x intercept of the function tell you in terms of age and height Would you expect such a point to exist The x intercept tells us I expect such a point to exist because For more information on this topic look in section 1 2 of your textbook especially at Example 7 You might also look at the Functions Domain and Range presentation

You and your friends get to go to an amusement park You have 75 for the day The entrance fee is 49 95 and lunch is 11 You want to be able to join your friends and play in the arcade Each game is 1 75 a Write an inequality to express the number of games you can play b How many games can you play Graph the solution interva number line on a sheet of paper Describe how your graph looks c After you have played in the arcade have you spent all your money if not how much is left over Explain your answer d If you want to play 2 more games to beat your record how much less will your lunch need to cost

12 You want to rent a tuxedo for a few weeks The rental company employee says it costs 94 to rent the tuxedo for one day and 23 for each additional day after the first Also you may only keep the tuxedo for a maximum of 40 days If you rent a tuxedo what is the range of the function O positive real numbers O all real numbers between 0 and 40 O all real numbers between 94 and 991 O all real numbers

Set a 0 and b 2 Find the area under fix by selecting the ff x dx option Find the area under g x by selecting the Sax dx between f x and g x by selecting the x a x dx option Use the interactive figure to find your answer f x dx 0 Type an integer or decimal rounded to three decimal places as needed 2 x dx 0 0 Type an integer or decimal rounded to three decimal places as needed 2 Sirx 9 x g x dx a 0 b 2 Areas of f x dx g z dz f f x g x dz O Show Values Large O dx option Find the area Area between Two Curves 1 14 12 10 8 6 IFig 4 35 f x x 4 Te g x x 1 3 4

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function Enter your answers as a comma separated lis y 7 sec 4x 7 0 56

Find the value of 15 000 at the end of one year if it is invested in an account that has an interest rate of 3 60 and is compounded in accordance with the rules below a compounded monthly b compounded daily assuming a 365 day year c compounded quarterly a What is the value if the money is compounded monthly Do not round until the final answer Then round to the nearest cent as needed b What is the value if the money is compounded daily 0 Do not round until the final answer Then round to the nearest cent as needed c What is the value if the money is compounded quarterly Do not round until the final answer Then round to the nearest cent as needed

Find the indicated derivative and simplify log 5x 5 y for y y 0 9 x

Evaluate the integral 3 Sxe x dx Xe 1 3 xe x dx Xe 1 Type an integer or decimal rounded to three decimal places as neede

A manufacturer incurs the following costs in producing x water ski vests in one day for 0 x 150 fixed costs 245 unit production cost 15 per vest equipment maintenance and repairs 0 05x dollars So the cost of manufacturing x vests in one given day is given by C x 0 05x 15x 245 where 0 x 150 A What is the average cost C x per vest if x vests are produced in one day B Find the critical numbers of C x the intervals on which the average cost per vest is decreasing the intervals on which the average cost per vest is increasing and the local extrema Do not graph A C x B Find the critical numbers of C x Select the correct choice below and if necessary fill in the answer box to complete your choice Use a comma to separate answers as needed OA The critical number s is are x OB There are no critical numbers of C x The average cost per vest is decreasing on the interval s Type your answer in interval notation Use a comma to separate answers as needed The average cost per vest is increasing on the interval s Type your answer in interval notation Use a comma to separate answers as needed Find the local extrema Select the correct choice below and if necessary fill in the answer boxes to complete your choice

A consulting firm using statistical methods provided a veterinary clinic with the cost equation C x 0 00047 x 200 304 560 100 x 1 000 C x where C x is the cost in dollars for handling x cases per month The average cost per case is given by C x X A Write the equation for the average cost function C x B Graph C on a calculator Choose the correct graph below OA 100 1000 by 0 3200 O B O C G Complete parts A through C SO D

400 for a company that manufactures tennis rackets the average cost per racket is found to be C X H hour Use the differential to approximate the change in average cost per racket if production is A increased from 20 per hour to 26 per hour and B increased from 40 per hour o 46 per hour A If production is increased from 20 per hour to 26 per hour the average cost per racket will 1 2 B If production is increased from 40 per hour to 46 per hour the average cost per racket will x for x 1 where x is the number of rackets produced per by approximately by approximately per racket per racket

Find A f x B the partition numbers for f and C the critical numbers of f f x x 27x 1 A f x B Find the partition numbers for f Select the correct choice below and if necessary fill in the answer box to complete your choice OA The partition number s is are x Use a comma to separate answers as needed OB There are no partition numbers C Find the critical numbers for f Select the correct choice below and if necessary fill in the answer box to complete your choice OA The critical number s is are x Use a comma to separate answers as needed B There are no critical numbers

The total sales of S in thousands of DVD s of a certain movie are given by the following formula where t is the number of months since the release of the DVD Use the formula to answer the questions 40t S t t 150 a Find S t S t b Find S 15 and S 15 The value of S 15 rounded to the nearest hundredth is The value of S 15 rounded to the nearest hundredth is What do the values for S 15 and S 15 indicate A After 15 months the total sales are 24 000 DVD s and the sales are increasing at the rate of 1 28 DVD s per month B After 15 months the total sales are 1280 DVD s and the sales are increasing at the rate of 24 DVD s per month OC After 15 months the total sales are 12 800 DVD s and the sales are increasing at the rate of 2400 DVD s per month

The total cost in dollars of manufacturing x auto body frames is C x 40 000 500x A Find the average cost per unit if 500 frames are produced Hint Recall that C x is the average cost per unit B Find the average value of the cost function over the interval 0 500 C Discuss the difference between parts A and B A The average cost per unit if 500 frames are produced is B The average value of the cost function is C C is the average cost per unit at a production level of 500 units is the average value of the total cost as production increases from 0 to 500 units

The total sales of a company in millions of dollars t months from now are given by S t 0 03t 0 8t 3t 4 A Find S t B Find S 2 and S 2 to two decimal places C Interpret S 11 173 73 and S 11 31 49 A S t B S 2 S 2 C Choose the correct interpretation of S 11 173 73 A In approximately 174 months the sales will be increasing by 11 million per month B In 11 months the sales will be increasing at a rate of 173 73 million per month OC The total sales 11 months from now will be 173 73 million dollars D In approximately 174 months the sales will be 11 million dollars Choose the correct interpretation of S 11 31 49 O A In approximately 31 months the sales will be 11 million dollars

Find each indicated quantity if it exists Let f x OA lim f x X 0 6x x 9 Simplify your answer 6x X 9 OB The limit does not exist if x 0 if x 0 A Select the correct choice below and if necessary fill in the answer box to complete your choice O A lim f x Simplify your answer X4 9 Complete parts A through C OB The limit does not exist B Select the correct choice below and if necessary fill in the answer box to complete your choice

triangle is placed in a semicircle with a radius of 3 cm as shown below Find the area of the shaded region Use the value 3 14 for and do not round your answer Be sure to include the correct unit in your answer 13 cm cm cm

Given the graph of a radical function which statement is correct 4 3 2 1 OR YER 4 3 2 1 2 3 7 OR YeRly 2 3 OR VERIy2 2 OR YER y21 2 3 4 5 6 7 8 9 x

Given two functions fx 2 x 1 3 and g x 2 log x 1 3 A Determine whether the following statements are true or false Explain your reasoning for each answer number your answers and show work when needed 1 f x and g x have the same end behavior 2 f x and g x both have domain restrictions 3 The average rate of change of f x on the interval from x 0 to x 8 is 2 4 Both f x and g x are always increasing B g x is a transformation of the parent function y log x Describe all transformations from the parent graph to the graph of g x Explain how you discovered each transformation

1 point Consider the function f x 3x 9 Its tangent line at x 4 goes through the points 9 y an 2 1 where y and y

eorge works at a factory where they make handmade b nd whistles The number of bells and whistles George m ach hour can be modeled by the equation b 2t where b is the number of bells and whistles and t is ne number of hours since he begins his shift 1 6 raph this situation on your calculator or on a sheet of p What is a reasonable domain and a reasonable range for tuation D t 8 R b 12 D 0 t 12 R 0 b 6 D 0 b 6 R 0 t 10 D b 10 R t 8

Use the trapezoidal rule the midpoint rule and Simpson s rule to approximate the given integral with the specified value of n Round your answers to six decimal places yc y cos y dy a the trapezoidal rule 2 364034 b the midpoint rule 2 310690 c Simpson s rule 2 346519 X n 8

a Find parametric equations for the line through 4 1 6 that is perpendicular to the plane x y 3z 1 Use the parameter t x t y t z t b In what points does this line intersect the coordinate planes xy plane x t y t z t yz plane xz plane x t y t z t x t y t z t K

Evaluate the integral 0 4T sin 2t dt

Evaluate the integral 10 x4x dx

Evaluate the integral 1 7 W w In w dw

1 Points DETAILS SCALCET9 7 1 008 Evaluate the integral Use C for the constant of integration x cos x dx

The widths in meters of a kidney shaped swimming pool were measured at 3 meter intervals as indicated in the figure below Use Simpson s rule with n 8 to estimate the area of the pool Round your answer to the nearest sq 6 2 m 7 2 6 8 5 6 5 0 4 8 4 8

The graph of the acceleration a t of a car measured in ft s2 is shown below Use Simpson s rule with n 6 to estimate the increase in the velocity in ft s of the car during the 6 second interval Round your answer to two decimal places ak 12 8 V 4 0 2 4 ft s 6 t seconds

1 Find the area between y 3x and y x from x 0 to x 3 2

Let f x 8x 8 9e Then the equation of the tangent line to the graph of f x at the point 0 1 is given by y mx b for m b

Find 5 5 sin 5x dx 5 sin 5x dx Submit Question

Find the average value fave of f x x5 between 1 and 1 then find a number c in 1 1 where f c fave fave

1 Let g x f t dt where f is the function whose graph is shown in the figure y 6 5 4 3 2 1 1 a Estimate g 0 g 2 g 4 g 6 and g 8 b Find the largest open interval on which g is increasing C Find the largest open interval on which g is decreasing d Identify any extrema of g e Sketch a rough graph of g V X

dx Find the general solution for the differential equation 9y Choose the correct answer below OA OB O C 16x 27 27x y 16 C C 27x y 16 y OD 16x 27 C C 8x

Evaluate the integral 2 m S x sin x cos x dx

Evaluate the integral using the following values 6 x dx 2 2 x dx 320 6 x dx 16 6 LOX dx 4

After Watching and answering questions on MyLab Statistics discuss your understanding of Quartiles Variation Measure of Dispersion and Standard Deviation The discussion should include answers to the questions below but is not limited to it for you may conduct additional research to add to your discussion Are sampling always reliable Why is standard deviation important Give specific examples to illustrate your understanding You must use complete sentences and correct grammar spelling Complete assignment as directed in document Save your electronic copy as RTF Rich Text Format everyone will be able to open the document Post upload attach your document in Discussion Board 1 A or B discussion forum in Discussion Board by the due PDF so that

A force of 20 lb is required to hold a spring stretched 2 in beyond its natural length How much work W is done in stretching it from its natural length to 6 in beyond its natural length X ft lb W 14 99

A 10 ft chain weighs 35 lb and hangs from a ceiling Find the work done in ft lb in lifting the lower end of the chain to the ceiling so that it s level with the upper end ft lb

A function is continuous nonnegative concave upward and decreasing on the interval 0 a Which of the following is true Left end point estimate is less than the right end point estimate Left end point estimate is greater than the right end point estimate Left end point estimate is the same as the right end point estimate

The graph of fis shown in the figure The shaded region A has an area of 5 5 and answer for part f to four decimal places a b d y e 234 x dx c 1 x dx 2 f x dx 2f x dx 13 1 x 3 f x dx B 56 X f The average value of f over the interval 0 61 is f x dx 12 5 Use this information to fill in the blanks Ro

A helicopter starting on the ground is rising directly into the air at a rate of 32 feet per second You are running on the ground starting directly under the helicopter at a rate of 8 feet per second Find the rate of change of the distance between the helicopter and yourself when the helicopter has risen to a height of 24 feet in the air assuming that initially it was 16 feet above you

Find the center vertices foci and asymptotes of the hyperbola x 9 x 1 25 Center 4 Acv 1 Vertices and 0 Foci and D and y 0 O