Differentiation Questions and Answers

Let f x 3x 8 and g x 5x 3 Find and simplify fog x O fog x 15x 17 O fog x 15x 5 O fog x 45x 240x 323 O fog x 15x 1

The base of a solid is the region in the xy plane bounded by the curves y 6y 101 and x y 26y 179 Every cross section of this solid perpendicular to the y axis and to the xy plane is a half disk with the diameter of the half disk sitting in the xy plane The volume of this solid is

Find the global maximum and minimum points of the function f x 2x 54x 7 on the interval 0 4 O O O The global minimum is 101 at x 3 The global maximum is 115 at x 3 The global minimum is 115 at x 3 The global maximum is 115 at x 3 The global minimum is 7 at x 0 The global maximum is 115 at x 3 The global minimum is 7 at x 0 The global maximum is 95 at x 4

Find all the critical numbers of f x 2x4 4x 3x 7 O x 1 and x 0 Ox 1 and x 1 O x 1 x 0 and x 1 O x 0 and x 1

Determine the local maximum and minimum values of f x x 9x 3 using the second derivative test when it applies O O Local minimum value is 18 at x 0 Local maximum value is 18 at x 6 Local maximum value is 18 at x 0 Local minimum value is 18 at x 6 Local maximum value is 3 at x 0 Local minimum value is 111 at x 6 Local minimum value is 3 at x 0 Local maximum value is 111 at x 6

a Use transformations to graph the function b Write the domain and range in interval notatio c Determine the vertical asymptote 8 6 4 2 8 a 4 00 P b domain 1 range 0 c vertical asymptote x 1 8 6

Find an equation of the plane The plane through the origin and the points 3 3 8 and 5 1 2

se the figure to approximate the value of the six trigonometric functions at 2 to the nearest tenth men use a calculator to approximate each of the six trigonometric functions at 2 0 5 0 5 Unit Circle Use the figure to approximate the value of the six trigonometric functions to the neare tenth sin 2 0 Round to one decimal place as needed

f x csc x and f a 11 find the exact value of the following a f a b f a f a 2x f a 4

Use the fact that the trigonometric functions are periodic to find the exact value of the expression Do not use a calculator 17x 4 CSC CSC 17x

Find the higher order derivative dx d 3x In 3x 3x 3x In 3x 0

Answer the following questions about the secant function a Is the secant function even odd or neither b Is the graph of the secant function symmetric With respect to what

f x 4ex 7ex 9 Which of the following shows how to find the derivative of f x A F x 7e 9 x 4e 4e dx O B F x 4x OC f x OD f x dx 4e 42 7 9 d dx The derivative of f x d 4x 76 9 7ex 9 d 7 9 4 4e dx dx 76 9 2 d dx 4ex 7ex 9 is 7ex 9 7 9 7 9 7 9

Find the derivative of y with respect to 0 y In 5 cos 50 dy

Maximum Revenue Jesaki Electronics manufactures and sells smartphones per week The weekly price demand and cost equations are respectively p 486 0 31 and C x 19 471 22 x Suppose Jesaki Electronics wants to maximize weekly revenue Compute the following quantities 1 How many phones should be produced each week phones Round to 2 decimal places 2 What price should Jesaki charge for the phones cent 3 What is the maximum weekly revenue Enter the result for 2 per phone Round to the nearest per week Round to the nearest cent

les Part 1 of 2 Points 0 of 5 Write a system of inequalities that describes all the given conditions and graph the feasible region of the system Joyce is the marketing director for a new company selling a fashion collection for young women and she wishes to place ads in two magazines magazine V and magazine E Joyce estimates that each one page ad in magazine V will be read by 1 7 million people and each one page ad in magazine E will be read by 1 1 million people Joyce wants to reach at least 7 million readers and to place at least 2 ads in each magazine Save Write a system of inequalibes that describes all the given conditions Let x represent the number of ads in magazine V and y the number of ads in magazine E Choose the correct answer below Round to two decimal places as needed lear all

Calculate the derivative of the following function y x 6x 4 7 ala 11

Calculate the derivative of the following function y cscx cotx dy

Use the graphing guidelines to make a complete graph of f f x 6x x 16 Choose the correct graph below OA 10 Q B 10 Q O C 140 Q 104 16 10

Evaluate the integral S sin x cos x dx using the fundamental theorem of calculus Discuss whether your result is consistent with the figure shown to the right 1 4 7x 4 S sin x cos x dx x 4 Is this value consistent with the given figure OA The value consistent with the figure because the area below the x axis appears to be equal to the area above the x axis OB The value is consistent with the figure because the total area can be approximated using a rectangle base x and height sin x 4 cos x 4 2 OC The value is not consistent with the figure because the total area could be approximated using a rectangle of base x and height sin z 4 cos x 4 2 OD The value is not consistent with the figure because the figure is a graph of the base function f x instead of a graph of the area function A x 27 y sin x cos x

The top six genres of podcasts in the year 2016 are listed in the table to the right Use this information to list the elements of the following set F the set of genres with more than 7 million subscribers Choose the correct answer below OA F Sports Comedy Fashion Gossip OB F Sports Comedy News Fashion OC F News Sports OD F Gossip Fiction Rank Genre 1 News Sports Comedy Fashion Gossip Fiction 23456 Subscriptio 21 953 00 19 092 000 13 763 000 12 188 000 4 720 000 4 523 014

3 Find the exact value Do not use a calculator Write undefined if it does not exist Show rough sketch of unit circle or bow tie as needed fan 2 slumotimane sin 1 2 sin sin 2 tan tan cot 1

Use factoring to solve the equation 12x 5x 2 0 1 2 The solution s is are x 4 3 Simplify your answer Use a comma to separate answers as needed

Find the maximum and minimum of to P 24x 21y subject 0 x 10 0 y 5 3x 2y 6

Solve each inequality log6 3 x log x 1 O x3 x22 no solution O x22 O x3 x Question 20 Evaluate each expression

Sketch the normal curve and shade the to find p z 2 85

For which interval is the average rate of change of f x negative

3 Find the first and second derivatives A f x 6x 4x x B g x 3x ln x

10 Answer 3 Step 2 of 2 Determine the value s of the local extrema you identified in the previous step Write DNE for all extrema that do not exist Separate multiple answers wit a comma if necessary Local minimum value s 31 Local maximum value s X Keyp Keyboard Shor

Solve the triangle b A C 1 95 Round to two decimal places as needed 41 2 Round to one decimal place as needed Round to one decimal place as needed O 2 40 3 b A

Find the derivative of 18 9x 4x 2 9x 1 9x 1 1 7 g x u 6 32 U 1

Solve the triangle A a 5 b 12 c 13 Round to one decimal place as needed

An ellipse with focal axis x hand semimajor axis length a has an equation of the form Select one O a O b OC O d y k x h 6 a y k x h a 62 y k b y k b x x h a x h a 1 1 1 1 A

Solve the following triangle A 20 B 10 a 7 C Simplify your answer ba Type an integer or decimal rounded to two decimal places as needed CR Tyne an integer or decimal rounded to two decimal places as needed

Find the derivative of y e5x cos 3x O O O dy dx dy dx dy dx dy dx 3e5x sin 3x 15sin 3x 5e 5x cos 3x 3e5 sin 3x 5e5x cos 3x 3e5xsin 3x

Determine whether the given sequence is arithmetic If the given sequence is arithmetic find the first term a and the common difference d 4 9 14 19 24 Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The sequence is arithmetic with first term and common difference Simplify your answer Type an integer or a fraction OB The sequence is not arithmetic

Find the derivative of f x sec x 5x 1 O f x 3x 5 sec x 5x 1 tan x 5x 1 O f x sec 3x 5 tan 3x 5 O f x sec x 5x 1 tan x 5x 1 O f x 3x 5 secxtanx

Find the third derivative of f x O f x O f x 1 36x f x 1 O f x 7sinx 36x 16 5 7sinx 16 7sinx 7sinx 2 3x 7cosx

Find the derivative of f x 3x5sinx 8cosx O f x 15x sinx 3x5cosx 8sinx O f x 15x sinxcosx 8sinx O f x 15x sinx 3x5cosx 8sinx O f x 15x sinxcosx 8sinx

Let y 8x 25x Find the differential dy Ody 16xe 25x 200x e25x dx O dy 16xe 25x 200x e25x Ody 400xe 25xdx Ody 16xe 25x dx

Find the derivative of f x O f x O f x 3 10x cosx 2x5 sinx 4 O f x 3 2x5 sinx 4 O f x 3 10x4 cosx 2x5 sinx 2 3 10x cosx 4 1 2x5 sinx 3

Find the derivative of f x arcsin 3x4 O O O dy dx dx O dx 72x7 1 9x8 1 1 9x dy 12x dx 1 9x8 8 3 12x 9x8 1

Using logarithmic differentiation find the derivative of y O O O O dy dx dy dx dy dx X 5 x5 tanx 4x 10 x 5 secxcscxX secxcscx 5 xtanx 5 4x 10 x 12x 4x 10 secxcscx dy 5 secxcscx dx X 12x 4x 10 12x 4x 10 3 12x 4x 10 xtanx 4x 10

Find the derivative of f x O f x 15x4 O f x O f x 48x5 150x 38 2x 5 O f x 48x5 150x4 38 2x 5 6x5 19 2x 5 48x5 150x4 38 2x 5

Find the derivative of g x O g x O g x g x 7 1 8 X O g x O g x 10 x 10x 1 7 8 1 X

01 6 O 6 O O 6 5 6 4 3 2 I 1 1 I T 1 2 0 1 2 3 4 5 6 1 2 Using the graph of f x x estimate the derivative of f x when X 2 3 4 5 6 X

Use the limit definition of the derivative to find f x when f x 6x O f x 12x 6h O f x 12x O f x 12x O f x 2x

Which of the following inferences about the Hunger Games is best supported by the rule change that two tributes from the same district can now win A The Hunger Games audience is rooting for Peeta and Katniss to be together B The Hunger Games audience is bored with this year s Games so the Gamekeepers need to shake things up with some new rules OC The Hunger Games is solely for punishment not entertainment D The Hunger Games has a long list of rules that frequently change

6 A nutritionist believes that having each player take a vitamin pill before a game enhances the performance of the football team During the course of one season each player takes a vitamin pill before each game and the team achieves a winning season for the first time in several years Is this an experiment or an observational study A An experiment but with no reasonable conclusion possible about cause and effect B An experiment thus making cause and effect a reasonable conclusion C An observational study because there was no use of a control group D An observational study but a poorly designed one because randomization was not used E An observational study thus allowing a reasonable conclusion of association but not of cause and effect 7 Researchers were interested to know whether internal vehicle temperatures vary by outside temperatures To evaluate this temperature rise was measured continuously over a 60 minute period in a dark sedan on 16 different clear sunny days with outside temperatures ranging from 72 F to 96 F the researchers method of analysis is best described as Pearson s test prep pg 67 3 A a census B a survey C an observational study D a randomized comparative experiment El a single blind randomized comport xperiment

The rate of markup on a bicycle selling for 845 is 32 Calculate the rate of margin For the toolbar press ALT F10 PC or ALT FN F10 Mac