Deck 3: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Question 1

Use Newton's method to approximate the given number correct to eight decimal places

A)
B)
C)
D)
E)

Answer 1

Question 2

The sum of two positive numbers is 16.What is the smallest possible value of the sum of their squares?

Answer 2

128

Question 3

Find f,

A)
B)
C)
D)
E) None of these

Answer 3

Question 4

Given that the graph of f passes through the point (4,69)and that the slope of its tangent line at is ,find f (1).

A) 6
B) 1
C) 12
D) 11
E) 0

Question 5

Find the position function of a particle moving along a coordinate line that satisfies the given condition. ,s(1) = -1

Question 6

A particle is moving with the given data.Find the position of the particle ,

A)
B)
C)
D)
E)

Question 7

Find the most general antiderivative of the function.

A)
B)
C)
D)
E)

Question 8

Find two positive numbers whose product is 121 and whose sum is a minimum.

A) 6,24
B) 2,72
C) 4,36
D) 11,11
E) 3,48

Question 9

A woman at a point A on the shore of a circular lake with radius 4 mi wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time.She can walk at the rate of 6 mi/h and row a boat at 2 mi/h .How should she proceed? (Find ).Round the result,if necessary,to the nearest hundredth.

A) 0.44 radians
B) She should walk around the lake from point A to point C.
C) 0.46 radians
D) She should row from point A to point C radians
E) 0.62 radians

Question 10

Use Newton's method with the specified initial approximation to find ,the third approximation to the root of the given equation.(Give your answer to four decimal places.)

Question 11

What constant acceleration is required to increase the speed of a car from 20 ft/s to 45 ft/s in 4 s?

Question 12

Use Newton's method with the specified initial approximation to find ,the third approximation to the root of the given equation.(Round your answer to four decimal places.)

A)
B)
C)
D)
E)

Question 13

Find f,

A)
B)
C)
D)
E)

Question 14

Find the position function of a particle moving along a coordinate line that satisfies the given conditions. ,s (0)= 5,v (0)= 0

Question 15

Find the most general antiderivative of the function.

Question 16

Find the point on the line that is closest to the origin.

A)
B)
C)
D)
E)

Question 17

A car braked with a constant deceleration of 40 ,producing skid marks measuring 60 ft before coming to a stop.How fast was the car traveling when the brakes were first applied?

Question 18

Use Newton's method with the specified initial approximation to find ,the third approximation to the root of the given equation.(Round your answer to four decimal places.)

A)
B)
C)
D)
E)

Question 19

Find the most general antiderivative of the function.

Question 20

Use Newton's method to approximate the indicated root of in the interval ,correct to six decimal places.
Use as the initial approximation.

Question 21

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

A)
B)
C)
D)
E)

Question 22

Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length L = 8 and width W = 3.

Question 23

The graph of the derivative of a continuous function f is shown.On what intervals is f decreasing? .

A)
B)
C)
D)
E) None of these

Question 24

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

A)
B)
C)
D)
E)

Question 25

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

A)
B)
C)
D)
E)

Question 26

Given
(a)Find the intervals on which f is increasing or decreasing.
(b)Find the relative maxima and relative minima of f.

A) (a)Increasing on ,decreasing on and
(b)Rel.max. , rel.min.
B) (a)Increasing on and decreasing on
(b)Rel.max. , rel.min.
C) (a)Increasing on and decreasing on
(b)Rel.max. , rel.min.
D) (a)Increasing on ,decreasing on and
(b)Rel.max. , rel.min.

Question 27

Given
(a)Find the intervals on which f is increasing or decreasing.
(b)Find the relative maxima and relative minima of f.

A) (a)Increasing on , Decreasing on
(b)Rel.min.
B) (a)Increasing on
(b)None
C) (a)Decreasing on
(b)None
D) (a)Increasing on , Decreasing on
(b)Rel.max.

Question 28

The function satisfies the hypotheses of Rolle's Theorem on the interval .Find all values of c that satisfy the conclusion of the theorem.

A) -5
B) -6
C) -6,-4
D) -5,-4

Question 29

The graph of the first derivative of a function f is shown below.At what values of x does f have a local maximum or minimum?

Question 30

Given . (a)Find the intervals on which f is increasing or decreasing.
(b)Find the relative maxima and relative minima of f.

A) (a)Increasing on , Decreasing on
(b)Rel.max.
B) (a)Increasing on , Decreasing on
(b)Rel.min.
C) (a)Increasing on , Decreasing on
(b)Rel.min.
D) (a)Increasing on , Decreasing on
(b)Rel.max.

Question 31

A farmer with 710 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.What is the largest possible total area of the four pens?

Question 32

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

A)
B)
C)
D)
E)

Question 33

What is the minimum vertical distance between the parabolas and ?

Question 34

A steel pipe is being carried down a hallway 14 ft wide.At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide.What is the length of the longest pipe that can be carried horizontally around the corner?

Question 35

Determine where the graph of the function is concave upward and where it is concave downward.Also,find all inflection points of the function.

A)
B)
C)
D)

Question 36

Given
(a)Find the intervals on which f is increasing or decreasing.
(b)Find the relative maxima and relative minima of f.

A) (a)Increasing on and ,decreasing on
(b)Rel.max. , rel.min.
B) (a)Increasing on and decreasing on and
(b)Rel.max. , rel.min.
C) (a)Increasing on and ,decreasing on and
(b)Rel.max. , rel.min.
D) (a)Increasing on ,decreasing on and
(b)Rel.max. , rel.min.

Question 37

Use the Second Derivative Test to find the relative extrema,if any,of the function .

A) Rel.max. , rel.min.
B) Rel.max. , rel.min.
C) Rel.max. , rel.min.
D) Rel.max. , rel.min.

Question 38

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

A)
B)
C)
D)
E)

Question 39

Find a cubic function that has a local maximum value of 115 at 1 and a local minimum value of -1,184 at 7.

Question 40

Find the maximum or minimum point(s)of the function

A)
B)
C)
D)
E)

Question 41

Find the critical numbers of .

A) 0,3,
B) 0,2,
C)
D) 0,2,
E) 0,3,

Question 42

Find the absolute maximum and absolute minimum values,if any,of the function on [0,25]

A) Abs.max. . abs.min.
B) Abs.max. . abs.min.
C) Abs.max. . abs.min.
D) Abs.max. . abs.min.

Question 43

The function satisfies the hypotheses of Rolle's Theorem on the interval .Find all values of c that satisfy the conclusion of the theorem.

A)
B)
C)
D)

Question 44

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.Then find all numbers c that satisfy the conclusion of Rolle's Theorem ,

A) ,
B) ,
C) ,
D) ,
E) None of these

Question 45

Find all the critical numbers of the function.

Question 46

Sketch the graph of on and find its absolute maximum and absolute minimum values,if any.

Question 47

Find the absolute minimum value(s) of on the interval [0,6].

Question 48

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. ,

A)
B)
C)
D)
E) None of these

Question 49

Find the critical number(s),if any of the function

A) 0,
B)
C) 0,
D)

Question 50

At 4:00 P.M. a car's speedometer reads 25 .At 4:15 it reads 72 .At some time between 4:00 and 4:15 the acceleration is exactly x .Find x.

Question 51

Find the critical number(s),if any,of the function .

A)
B)
C) None of these
D)

Question 52

Find the critical number(s),if any,of the function

A)
B)
C)
D) -4

Question 53

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.Then find all numbers c that satisfy the conclusion of Rolle's Theorem

A)
B)
C)
D)
E)

Question 54

Find the critical numbers of the function.

Question 55

The graph below is the graph of function f on the interval Find the absolute maximum and absolute minimum values of f (if they exist)and where they are attained.

Question 56

Find the absolute maximum and absolute minimum values,if any,of the function on .

A) Abs.max. . abs.min.
B) Abs.max. https://d2lvgg3v3hfg70.cloudfront.net/TB2067/. abs.min.
C) Abs.max. https://d2lvgg3v3hfg70.cloudfront.net/TB2067/. abs.min.
D) Abs.max. https://d2lvgg3v3hfg70.cloudfront.net/TB2067/. abs.min.