Application of derivatives Questions and Answers

Use properties of limits to find the indicated limit It may be necessary to rewrite the expression before limit properties can be applied x 6x 27 x 9 lim x 3 Select the correct choice below and if necessary fill in the answer box to complete your choice O A x 6x 27 9 Type an integer or a simplified fraction lim x 3 B The limit does not exist and is neither nor o

c r 3 sin 30 0 0 360 30 45 60 90 120 135 150 30 T 8 180 210 225 240 270 300 315 330 30 T 150 165 180 195 135 210 120 225 105 90 240 255 70 Dor 285 270 2 30 300 1 5 En 345 330 315

3 273 2 R x 5x 10x C x 5x 5 The y intercept of C x is at y 54 6 Simplify your answer Graph C x Choose the correct graph below A Ay 80 0 0 32 Q b Find the minimum break even quantity 22 Using the expressions OB AY 80 0 32 SOU Q G Type an equation Use integers or fractions for any numbers in the equation C Ay 80 32 3 273 10x and or 5x 5 identify an equation to be solved in order to find the minimum break even quantity OD Ay JLS 80 0 0 X 32

a Graph both functions Identify the vertex of R x The vertex of R x is 12 5 62 5 Type an ordered pair Simplify your answer Type integers or decimals Graph R x Choose the correct graph below O A Ay 80 0 X 32 OB Ay 80 0 0 21 32 C AY 40 0 0 16 OD 32 of 0 0 80

10 115 5 5 10 tion will display any text boxes needed to complete your answer Increasing on one interval Decreasing on one interval Constant on one interval O Increasing on one interval and Decreasing on another Increasing on two intervals 5 Increasing on Decreasing on

der the following graph of g x Write a formula for g x that describes the transformations performed on the basic function 10 5 5 Enable Zoom Pan 10 X

Question 15 of 15 Step 1 of 2 Y Answer 10 Step 1 of 2 Use the graph to determine the locations and type of the local extrema Write DNE for all extrema that do not exist Separate multiple answers with a comma if necessary Local minimum at 5 Local maximum at 12 17 Correct 0 Keypad Keyboard Shortcut

10 Answer 5 Trop Local minimum at S 5 12 17 Correct Step 1 of 2 Use the graph to determine the locations and type of the local extrema Write DNE for all extrema that do not exist Separate multiple answers with a comma if necessary 10 Keypac Keyboard Shortc

The function f is given by the graph below 10 Answer af NGAJ S 10 Enable Zoom Pan 5 Step 1 of 2 Use the graph to determine the locations and type of the local extrema Write DNE for all extrema that do not exist Separate mul comma if necessary

10 mswer S Local minimum value s 10 17 Correct 10 tep 2 of 2 Determine the values of the local extrema you identified in the previous step Write DNE for all extrema that do not exist Separate muldple answers with omma if necessary G Key Keyboard Shor

What is the average rate of change of f x from x 5 9 to x 3 6 Please write your answer rounded to the nearest hundredth f x 6x 5x 1 Answer

f x 12x 2 2x 2 find the equation of the tangent line x 9

Answer 10 5 Selecting an option will display any text boxes needed to complete your answer O Increasing on one interval Decreasing on one interval O Constant on one interval 5 10 5 Increasing on one interval and Decreasing on another Increasing on two intervals Decreasing on two intervals 10 x

The basic graph off x Answer is shown Manipulate the graph of f x to display the graph of g x Points can be moved by dragging or using the arrow keys k 10 s x 6 Enable Zoom Pan S

Consider the following function x x 3 4 Step 1 of 2 Determine the more basic function that has been shifted reflected stretched or compressed Answer f x

Consider the following function M x x 3 4 Step 1 of 2 Determine the more basic function that has been shifted reflected stretched or compressed Answer

A right triangle has a hypotenuse of length 9 inches If one angle is 39 find the length of each leg The length of the shorter leg is inches and the longer leg is inches Do not round until the final answer Then round to the nearest tenth as needed

The function f is given by the graph below 10 2023 Hawkes Learning 5 101 Enable Zoom Pan Step 1 of 2 Use the graph to determine the locations and type of the local extrema Write DNE for all extrema that do not exist Separate multiple answers wil comma if necessary MacBook Pro V Submi

A product is introduced into the market Suppose a product s sales quantity per month q t is a function of time t in months is given by q t 5000t 170t And suppose the price in dollars of that product p t is also a function of time t in months and is given by p t 170 t A Find R t the rate of change of revenue as a function of time t 680 150002 57800t 850000F expanding and collected not required B What is the the rate of change of revenue with respect to time 5 months after the introduction 271000 C Interpret your answer in part B include the units of the number in part B

The angle of inclination from the base of skyscraper A to the top of skyscraper B is approximately 11 3 If skyscraper B is 1445 feet tall how far apart are the two skyscrapers Assume the bases of the wo buildings are at the same elevation The distance from skyscraper A to skyscraper B is Round to buo decimal places as needed feet

se the triangle shown on the right and the given information to solve the triangle c 2 B 40 find a b and A

Complete the sentence given below In a right triangle the sum of the two acute angles is degrees

The university is adjusting to COVID 19 With 84 linear feet of plexiglass panels they plan to fence a region for six individuals to sit and listen to calculus lectures without infecting each other as shown in the sketch Y If it is to be maximized what is the total area in square feet of all six enclosed regions square feet What is the optimal value of a that gives this maximum area

et v 3 V 7 6 V3 8 2 9 and H Span V V V3 It can be verified that 7v 8v 3v3 0 Use this information to find a basis for 5 basis for H is ype an integer or decimal for each matrix element Use a comma to separate vectors as needed

particle moves with a velocity of t ft s along an axis Find the displacement and the distance traveled by the particle during the given time interval Give exact answ u t t t 0 t 4 a Displacement b Distance include units include units

Determine where the function f x is decreasing if the first derivative is f x xe x 1 x 1 Enter your answer using interval notation such as 4 9

In 1997 researchers at Texas A M University estimated the operating costs of cotton gin plans of various sizes A quadratic model of cost in thousands of dollars for the largest plants was found to be very similar to C q 0 022q 20 2g 307 where q is the annual quanity of bales in thousands produced by the plant Revenue was estimated at 60 per bale of cotton Find the following but be cautious and play close attention to the units A The Marginal Cost function MC q 0 044g 20 2 B The Marginal Revenue function MR q 60 C The Marginal Profit function 0 044g 80 2 MP q X D The Marginal Profits for q 452 thousand bales MP 452 Round to the nearest penny if necessary see Part E for units E Which of the following represent the proper measurement units for the answer to Part D thousands of dollars per unit dollars per unit units per dollar units dollars

Which of the following scenarios best illustrates how reputation is a powerful motivator for cooperation a A woman risks her life by traveling into flooded areas during a hurricane to help rescue stranded strangers b A group of teenagers bully an unpopular peer on a public bus but none of the other passengers help because they assume someone else will Oc A man resigns from his job and moves across the country to help his favorite uncle recover from alcoholism d A woman refuses to lend her colleague money because the colleague still has unpaid debts to other people they know

car traveling at 48 ft sec decelerates at a constant 8 feet per second per second How many feet does the car travel before coming to a complete stop 1

A rectangle is inscribed under the graph of f x 9 x in the first quadrant x 9 x Determine the value of that maximizes the area of the rectangle under f x 9 having lower left corner 0 0 and upper right corner x 9 x

v x 6 x 3 tep 3 of 4 Graph the given function by indicating how the more basic function has been shifted reflected stretched or compressed nswer Keyboar Select the type of transformations to create the correct graph Any further inputs required to complete the transformations will appear when the appropriate sel made Horizontal Shift O Left Vertical Stretch Compress Stretch x Axis Reflection Yes Right y Axis Reflection Yes Compress None No None O No 10 5 Si 5 Enable Zoo Pan Enable Zoom and Pan 4

ep 3 of 4 Graph the given function by indicating how the more basic function has been shifted reflected stretched or compressed swer lect the type of transformations to create the correct graph Any further inputs required to complete the transformations will appear when the appropriate selectie ade Horizontal Shift Left Vertical Stretch Compress Stretch O Right x Axis Reflection Yes Yes y Axis Reflection Vertical Shift Up O No Compress None No None Down None 10 5 s 10 Enable Zoom Pan 10 NO k Keyboard Sa

Eric purchased 4 presents on layaway that cost 15 70 18 50 21 00 and 26 40 If he made an initial deposit of one third of the total amount and the rest in 4 equal weekly payments how much was each of the 4 wedkly payments a 27 20 b 15 40 c 54 40 d 13 60 e 20 40

Suppose that x y 2 and dx Find when x 2 dt dy dt

The graph of f x is given Points A 2 1 B 0 0 C 3 3 and D 6 0 are labeled Where does f x have a inflection point on the interval 4 7 f x x 2 Point A Ox 0 Point B Ox 3 Point C Ox 6 Point D Some other point not labeled O More than one point O No points O Not enough information is given 2 A B 3 D 7 I

Find the derivative of the following function using the Fundamental Theorem of Calculus F m F x f 2t 1 dt

Consider the following function v x 6x 3 Step 1 of 4 Determine the more basic function that has been shifted reflected stretched or compressed Answer

probability of rolling a l or a 4 Write your answer as a fraction 4 Assuming there is a 0 5 probability that a coin will land on heads what is the probability that flipping a coin will land on heads then heads then tails and then heads again

8 90 The middle term of 5x DSO 56x y D 70x B E 70x y 1 680x y C 56

2T Evaluate the integral c 0 Answer 3 cos x dx

Evaluate the definite integral Your answer will be a function of z 6t 6t 1 dt

The financial office at a large university claims that the average cost of textbooks per semester for students is 350 The campus newspaper wants to verify if the claim is true Using a sample of 60 students the newspaper calculated a sample mean of 400 Based on this information we can safely conclude that the university s claim that the mean textbook expenditure of 350 is not justified True False 3

Select the indicated term for each binomial expansion below The 7 term of x x A 6 435x D 6 435x 7 90 B 3 003x E 5 005x C 5 005xy

A medical equipment industry manufactures X ray machines The unit cost C the cost in dollars to make each X ray machine depends on the number of machines made If x machines are made then the unit cost is given by the function C x 0 7x 210x 27 738 What is the minimum unit cost Do not round your answer

baseball team plays in a stadium that holds 1 000 spectators With the ticket price at 10 the average attendance at recent ames has been 33 000 A market survey indicates that for every dollar the ticket price is lowered attendance increases by 3000 a Find a function that models the revenue in terms of ticket price Let x represent the price of a ticket and R represent the revenue R x 51000x 3000x b Find the price that maximizes revenue from ticket sales 8 5 x c What ticket price is so high that no revenue is generated 17

0 3t The concentration of a drug t hours after being injected is given by C t t 49 concentration is at a maximum Give your answer accurate to at least 2 decimal places Find the time when the hours

The given curve is rotated about the y axis Find the area of the resulting surface X Va y 0 y a 6

Find the effective rate corresponding to the given nominal rate Round your answers to three decimal places a 5 5 year compounded monthly b 5 5 year compounded daily

Find the interest rate needed for an investment of 6 000 to grow to 8 000 in 10 years if Interest is compounded continuously Round your answer to the nearest hundredth of a percentage poi 2 87 X

a Identify the center of the ellipse c Identify the endpoints of the minor axis e Graph the ellipse Express numbers in exact simplest form x 4 y 4 16 Part 1 of 5 The center of ellipse is 0 4 Part 2 of 5 The vertices are 4 4 and Part 2 5 Part 3 of 5 4 4 The endpoints of the minor axis are 2 3 b Identify the vertices d Identify the foci and 2 3 3 16 X G