Calculus Questions

23 f x 25 f x A B Cex X X X 24 f x 26 f x 1 xe x ex ax b CX d

1 Find the derivative of y x 1 x 1 in two ways by using the Product Rule and by performing the multiplication first Do your answers agree 2 Find the derivative of the function F x x 3x x x in two ways by using the Quotient Rule and by simplifying first Show that your answers are equivalent Which method do you prefer

3 26 Differentiate 3 f x x 2x e 5 y X 4 g x x ex ex 1 X 6 y

What is p x when p x log4 Select the correct answer below O p x O p x O p x O p x 12x 5 6x 5x 2 x 4ln 4 6x 5x 2 6 I 1 6x 5x 2 ln 4 12x 5 6x 5x 2 ln 4 1 6 zln 4 6 ln 4 6x 5x 2 x64 1 1

Find the derivative of 6 O In 6 6 O In 6 6 O 6 In 6

If r x logs 2x 3x 1 find r x Select the correct answer below In 8 6x 62 2r 3r2 1 O logs 6x2 6x O O 1 In 8 22 3x 1 6r 4 62 In 8 22 3r2 1 2r 3x2 1

Consider the following rational expression Step 2 of 2 Determine what value s if any of the variable must be excluded Answer Select the number of values that must be excluded 27x 64 3x 4 Selecting an option will display any text boxes needed to complete your answer 00 1 02 03

x 1 What is the first derivative of g x ln 1 Select the correct answer below 3x Og x x 1 3x x 1 Og x Og x Og x x 1 3x 3x x 1 473 x 1 4x 2 1 x 1 4x 47 1

27x 6 3x 4

Graph the function f x x 6x by starting with the graph of y x and using transformations shifting stretching compressing and or reflecting Use the graphing tool to graph the function Click to enlarge graph Ay SHEEPSK 30 20

The monthly revenue R achieved by selling x wristwatches is figured to be R x 71x 0 2x The monthly cost C of selling x wristwatches is C x 30x 1750 a How many wristwatches must the firm sell to maximize revenue What is the maximum revenue b Profit is given as P x R x C x What is the profit function c How many wristwatches must the firm sell to maximize profit What is the maximum profit d Provide a reasonable explanation as to why the answers found in parts a and c differ Explain why a quadratic function is a reasonable model for reventa a The firm must sell wristwatches to maximize revenue Round to the nearest integer as needed The maximum revenue is Round to two decimal places as needed

Multiply or divide the following rational expressions as indicated and simplify your answer x 7x 12 x 4 27 x 3x 18 x 4

Graph the function f x x 2 4 by starting with the graph of y x and using transformations shifting stretching compressing and or reflecting Use the graphing tool to graph the function Click to enlarge graph 10 6 4 10 8

What is t x when t x ln In 2 3 2 2 Select the correct answer below O t x 2 O t x 2 O t x O t x 2x 4x 3 2x 3x 2 4x 3 2x 3x 2 2r 3x 2 4x 3 4x 3 2x 3x 2

Question 5 of Add or subtract the following rational expressions as indicated and simplify your answer y 3 35 Answer y 2 y 3 2 y2 2y 31

Graph the following function by starting with the graph of y x and using transformations shifting compressing stretching and or reflection 52 f x 4x Lan the graphing tool to graph the function

Solve the following quadratic like equation Te

If t x ln find t x A 2 1 Select the correct answer below t x 1 2 2 1 O I 2x O t x x t x t x 1 2 O t x 2x x 1 2x x 1 2x x 1

9 16 Find the intervals on which f is increasing or decreasing and find the local maximum and minimum values of f 9 f x 2x 15x 24x 5 10 f x x 6x 135x 11 f x 6x4 16x 1 x 24 x 5 13 f x 12 f x x x 3 4 14 f x x 2 X

What is the first derivative of h x 4 Select the correct answer below h x 4 x 4ln 9 h x x 4 1 Oh x 4 2 28 9ln 4 O h x ln 4 4 2 h x 9x 4 x

A roast turkey is taken from an oven when its temperature has reached 185 F and is placed on a table in a room where the temperature is 75 F Round your answers to the nearest whole number a If the temperature of the turkey is 150 F after half an hour what is the temperature after 60 minutes T 60 F b When will the turkey have cooled to 90 t min

Find the derivative of f x e22 x

Sud udv uv va Seec 3x dx

Differentiate f x the function f x sin 7 In x 7 cos 7 ln x

Solve for x over the complex numbers 4x 13 0 Enter your answers in the boxes in standard form or x

u cos2x dv 4x 4x cos2x dx du V Seurax ife U 4x du 4 dx 2sin 2x elix 4 du Scos2x Seas 4x e4x 47 e4x cos 2x 4 cos 2x 4 cos 2x cos 2x LX e ex sin 2x 8 4X U 2sin 2x du 4052 dv e4xs 4 V e x 16 4x 23 in 23 e4x fett 7 16 16 4cos2x 2 sin 2x sin 2x S 1 4x cos2x dx 4x e4 cos 2x 4

In each part state the x coordinates of the inflection points of f Give reasons for your answers a The curve is the graph of f b The curve is the graph of f c The curve is the graph of f YA 0 2 4 6 8 X

1 2 Use the given graph of f to find the following a The open intervals on which f is increasing b The open intervals on which f is decreasing c The open intervals on which f is concave upward d The open intervals on which f is concave downward e The coordinates of the points of inflection 1 y 2 y 1 0 1 x 4 a State the First Derivative Test b 5 yt 1 0 3 Suppose you are given a formula for a function f a How do you determine where f is increasing or decreasing b How do you determine where the graph of f is concave upward or concave downward c How do you locate inflection points 1 State the Second Derivative Test Under what circum stances is it inconclusive What do you do if it fails y f x 5 6 The graph of the derivative f of a function f is shown a On what intervals is f increasing Decreasing b At what values of x does f have a local maximum Local minimum X 6 YA 2 YA 0 y f x 7 In each part state the x coordinates of the inflection points of f Give reasons for your answers a The curve is the graph of f b The curve is the graph of f c The curve is the graph of f 2 4 4 6 X m 6 8 8 The graph of the first derivative f of a function f is shown a On what intervals is f increasing Explain b At what values of x does f have a local maximum or minimum Explain y f x X c On what intervals is f concave upward or concave downward Explain d What are the x coordinates of the inflection points of f Why

The square root of a number is greater than the square of the number For what set of numbers is this true 0 1 O 0 1 O 1 00 O 1 00

A vitamin degrades in the body according to the function represented in the table where x is the time in hours and f x is the dosage in milligrams X 0 4 8 12 24 500 00 158 20 50 06 15 8 0 50 What was the original dose O 0 50 milligrams O 8 milligrams O24 milligrams 500 milligrams

d Find the rate of growth after 8 hours Round your answer to three decimal places billion cells per hour e When will the population reach 20 000 cells Round your answer to two decimal places hr Submit Answer 25 Points DETAILS SCALCET8 3 8 010 A sample of a radioactive substance decayed to 96 5 of its original amount after a year Round your answers to two decimal places a What is the half life of the substance yr b How long would it take the sample to decay to 75 of its original amount yr Submit Answer

The inequality log 2x 7 2 3x 2 can be broken into two related inequalities Review the graphs of the two related inequalities 5 4 3 2 1 5 4 3 2 2 3 5 y 1 2 3 5 X Based on the graph which set shows the solution to log 2x 7 2 x 2 O 00 00 O 3 5 1 5 O 3 5 00 O 1 5 00

f x h f x a 5pts Find the average rate of change between x 1 and x 2 2 25 4 2 2 11 4 1 Tim 2 x h 4 x h 2x 4x 470 2 3 2x 2xhth 4 4h 2x 4x impo 2xhth 4h lim 70 h 2xth 4 3 f 2 F 1 X b X a im 2 1 0 4 6 h 0 b 5pts Find the average rate of change between x 1 and x 1 h30 C 5pts Find the instantaneous rate of change at x 1 f x th f x lim h30 2 1 2 1 f b Fla Xb X a 4 1 im 2 xth 4 x h 2x 4x h 0 linn 70 2x2 4 xhth 4x 4h 2x 4X h xhth 4h 7 h 1 h 4 1 0 4 8

An investor has purchased 1 000 shares of stock at a price of 10 per share The stock pays no dividends and historically has a growth rate of 12 5 per year compounded continuously Which function models this scenario O A t 1 000e12 5t O A t 1 000e 0 125 OA 10 000e12 5t A t 10 000e 0 125t

Submit Answer 12 5 25 Points DETAILS PREVIOUS ANSWERS SCALCET8 3 8 017 PRACTICE MY NOTES When a cold drink is taken from a refrigerator its temperature is 5 C After 25 minutes in a 20 C room its temperature has increased to 10 C Round your answers to two decimal places a What is the temperature of the drink after 40 minutes 12 15 X

Edmundo used a number line to show the solution for the inequality 12x 61 4 Which number line shows the solution O 6 5 4 3 2 1 0 1 2 3 4 5 6 6 5 4 2 1 0 1 2 3 4 5 6 8 5 4 3 2 1 0 1 2 3 4 5 6 6 5 4 3 2 1 0 1 2 3 4 5 6

How many integers satisfy the inequality x2 4 x2 10 0 Onone Otwo four an infinite number

Find y and y y y y x In 6x

If f x n x find f 1 f 1 9 Submit Answer

Differentiate f x the function f x sin 7 In x

Let f x cx In cos x For what value of c is f 4 1 C Submit Answer

Derivative of an inverse function The function x x 1 is one to one for x 0 and has an inverse on that interval Find the slope of the curve y f x at the point 3 1 x 2 1 1 3 3 1 4 y f 6 X 9 xy 1 x 10 yz g metb m tan 1 THEOREM 3 21 Derivative of the Inverse Let f be differentiable and have an inverse which f x 0 then is differentia

a b The derivative can be used to find the O a point of intersection b common factors d Both b and c are correct What value is the following limit calculating O ld c instantaneous rate of change lim 4th 4 h 0 0 for f x x 4 fi 4 for f x x ft 16 for f x x fi 4 for f x x lim fiz h f x h lim h e h ho IC lim h f a h 0 h A notation for derivative a f x d dy da The derivative of a function f in terms of a limit is defined by which of the following lim f x f a a 20 b lim c fd x

Derivatives involving the inverse sine Compute the following deriva d dx sin x 1 b cos sin x oof n

Derivatives of an inverse function Use the values of a one to one d ferentiable function fin Table 3 7 to compute the indicated derivatives or state that t derivative cannot be determined a 5 Table 3 7 X f x x 1 2 1 2 b 2 0 3 2 1 5 3 2 C 2 6 3 7 2 3

If g x ln x 5x find g x 1 24 52 O O g x g x O g x g x 450 4x 5 4x 5 x4 5x 1 4x 5

Find the derivative of 5 O 5 O In 5 5 O ln 5 5 O 5 In 5

If x 9 find x O f x 4x 948 1 O f x 4 ln 9 94 Of x 9In 4 94 Of x 4 94

Find the derivative of log x O In 7 O 30 7x 30 1 x In 7

Let h x f x g x If f x 4x 3x and g x In 3x 1 what is h x Select the correct answer below Oh x 3 8x In 3x 1 Oh x 8x 3 3x 1 Oh x 8x 3 In 3x 1 Oh x 8x 3 In 3x 1 Oh x 8x 3 ln 3x 1 12x 9x 1 3x 12x 9x 3x 1 4x 3x 3x 1 12x 9x 3x 1 12x 9x 3x 1