Question 1

Use a graphing utility to estimate the absolute maximum of f(x) = x5 ln x on [1, 5].

Accepted Answer

Question 2

f(x) = cos 4x. Find the points of inflection on [0,  $\pi$/2].

Accepted Answer

The answer of f(x) = cos 4x. Find the points...

Question 3

The equation, x3 - 2x - 19 = 0 has one real solution for 1 < x < 19. Approximate it by Newton's Method. Use 4.75 for your initial value and calculate eight iterations.

Accepted Answer

f(x) = x³ - x - 19 f '(x) = 3

Question 4

Verify that f(x) = x2 + 8 satisfies the hypothesis of the Mean-Value Theorem on the interval [0, 4] and find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

f(0) = 8
f

Question 5

Use Newton's Method to find the largest positive solution of x4 -8x2 - 11 = 0.

Accepted Answer

A)  3.390625 
B)  3.0325159 
C)  3.1034671 
D)  3.0360381 
E)  3.0325251 
A)  3.390625 
B)  3.0325159 
C)  3.1034671 
D)  3.0360381 
E)  3.0325251

Question 6

The largest open interval over which f is concave up for f(x) = 4x3 + 8x2 - 7x + 2 is

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Use Newton's Method to find the largest positive solution of x4 + 5x- 3 = 0.

Accepted Answer

A)  0.5777207 
B)  0.9770528 
C)  1.4919618 
D)  2.1408010 
E)  2.9540230 
A)  0.5777207 
B)  0.9770528 
C)  1.4919618 
D)  2.1408010 
E)  2.9540230

Question 8

Find the value c that satisfies Rolle's Theorem for f(x) = cos 4x on   .

Accepted Answer

A)    
B)  4 $\pi$ 
C)  0 
D)    
E)    
A)    
B)  4 $\pi$ 
C)  0 
D)    
E)

Question 9

Find the location of the absolute maximum of 4 tan x on [0,  $\pi$], if it exists.

Accepted Answer

A)  4 
B)   $\pi$ 
C)  1 
D)    
E)  None exist. 
A)  4 
B)   $\pi$ 
C)  1 
D)    
E)  None exist.

Question 10

Given y = x2/3(x + 4). Plot any stationary points, inflections points, and cusps which may or may not exist. Approximate answers to 4 decimal places.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Relative maximum at (-1.6, @#IMG-DLM&

Question 11

Find all relative extrema of f(x) = 7x2 - 28x + 2.

Accepted Answer

Relative m

Question 12

The polynomial function x2- 4x + 1 has

Accepted Answer

A)  one stationary point that is at x = 4 
B)  one stationary point that is at x = -2 
C)  two stationary points, one at x = 0 and one at x = 4 
D)  two stationary points, one at x = 2 and one at x = -2 
E)  one stationary point that is at x = 2 
A)  one stationary point that is at x = 4 
B)  one stationary point that is at x = -2 
C)  two stationary points, one at x = 0 and one at x = 4 
D)  two stationary points, one at x = 2 and one at x = -2 
E)  one stationary point that is at x = 2

Question 13

Find the point on the curve x2 + y2 = 36 closest to (0, 8).

Accepted Answer

Question 14

Use a graphing utility to generate the graph of f(x) = x4 -6x3 + 11x2 - 12x + 7, then determine the x-coordinates of all relative extrema on (-10, 10) and identify them as relative maxima or relative minima.

Accepted Answer

A)  There is a relative maximum at x = 3. 
B)  There is a relative minimum at x = 0. 
C)  There is a relative maximum at x = 0. 
D)  There is a relative minimum at x = 3. 
E)  There are no relative extrema. 
A)  There is a relative maximum at x = 3. 
B)  There is a relative minimum at x = 0. 
C)  There is a relative maximum at x = 0. 
D)  There is a relative minimum at x = 3. 
E)  There are no relative extrema.

Question 15

If f(x) = (x -4)4 + 7 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

The answer of If f(x) = (x -4)4 + 7...

Question 16

Find the relative extrema for   .

Accepted Answer

Relative maximum at

Question 17

A rectangle is to have an area of 98 in2. What should be its dimensions if the distance from one corner to the mid-point of a nonadjacent side is to be a minimum?

Accepted Answer

Let x, y, and D be as shown in

Question 18

Answer true or false. f(x) = ln 6x has a point of inflection.

Accepted Answer

A) True 
 B)False

Question 19

The graph represents a position function. Determine what is happening to the velocity at t = 1.

Accepted Answer

A)  It is negative 
B)  It is positive 
C)  It is zero 
D)  There is insufficient information to tell. 
E)  It is +$\infty$ 
A)  It is negative 
B)  It is positive 
C)  It is zero 
D)  There is insufficient information to tell. 
E)  It is +$\infty$

Question 20

The graph below depicts the position function of a particle moving on a coordinate line at three different times. For each time specify whether the particle is moving to the left or right (Assume right is the positive direction.) and whether or not it is speeding up or slowing.

Accepted Answer

At t₁: The particle is moving to the left

Use a graphing utility to estimate the absolute maximum of f(x) = x⁵ ln x on [1, 5].

f(x) = cos 4x. Find the points of inflection on [0, $\pi$ /2].

The equation, x³ - 2x - 19 = 0 has one real solution for 1 < x < 19. Approximate it by Newton's Method. Use 4.75 for your initial value and calculate eight iterations.

Verify that f(x) = x² + 8 satisfies the hypothesis of the Mean-Value Theorem on the interval [0, 4] and find all values of C that satisfy the conclusion of the theorem.

Use Newton's Method to find the largest positive solution of x⁴ -8x² - 11 = 0.

The largest open interval over which f is concave up for f(x) = 4x³ + 8x² - 7x + 2 is

Use Newton's Method to find the largest positive solution of x⁴ + 5x- 3 = 0.

Find the value c that satisfies Rolle's Theorem for f(x) = cos 4x on .

Find the location of the absolute maximum of 4 tan x on [0, $\pi$ ], if it exists.

Given y = x^2/3(x + 4). Plot any stationary points, inflections points, and cusps which may or may not exist. Approximate answers to 4 decimal places.

Find all relative extrema of f(x) = 7x² - 28x + 2.

The polynomial function x²- 4x + 1 has

Find the point on the curve x² + y² = 36 closest to (0, 8).

Use a graphing utility to generate the graph of f(x) = x⁴ -6x³ + 11x² - 12x + 7, then determine the x-coordinates of all relative extrema on (-10, 10) and identify them as relative maxima or relative minima.

If f(x) = (x -4)⁴ + 7 , find the intervals where f is concave up and where f is concave down.

Find the relative extrema for .

A rectangle is to have an area of 98 in². What should be its dimensions if the distance from one corner to the mid-point of a nonadjacent side is to be a minimum?

Answer true or false. f(x) = ln 6x has a point of inflection.

The graph represents a position function. Determine what is happening to the velocity at t = 1.

The graph below depicts the position function of a particle moving on a coordinate line at three different times. For each time specify whether the particle is moving to the left or right (Assume right is the positive direction.) and whether or not it is speeding up or slowing.

Limits and Continuity

The Derivative

Topics in Deifferentiation

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 4: The Derivative in Graphing and Applications

Use a graphing utility to estimate the absolute maximum of f(x) = x5 ln x on [1, 5].

f(x) = cos 4x. Find the points of inflection on [0, π\piπ /2].

The equation, x3 - 2x - 19 = 0 has one real solution for 1 < x < 19. Approximate it by Newton's Method. Use 4.75 for your initial value and calculate eight iterations.

Verify that f(x) = x2 + 8 satisfies the hypothesis of the Mean-Value Theorem on the interval [0, 4] and find all values of C that satisfy the conclusion of the theorem.

Use Newton's Method to find the largest positive solution of x4 -8x2 - 11 = 0.

The largest open interval over which f is concave up for f(x) = 4x3 + 8x2 - 7x + 2 is

Use Newton's Method to find the largest positive solution of x4 + 5x- 3 = 0.

Find the value c that satisfies Rolle's Theorem for f(x) = cos 4x on .

Find the location of the absolute maximum of 4 tan x on [0, π\piπ ], if it exists.

Given y = x2/3(x + 4). Plot any stationary points, inflections points, and cusps which may or may not exist. Approximate answers to 4 decimal places.

Find all relative extrema of f(x) = 7x2 - 28x + 2.

The polynomial function x2- 4x + 1 has

Find the point on the curve x2 + y2 = 36 closest to (0, 8).

Use a graphing utility to generate the graph of f(x) = x4 -6x3 + 11x2 - 12x + 7, then determine the x-coordinates of all relative extrema on (-10, 10) and identify them as relative maxima or relative minima.

If f(x) = (x -4)4 + 7 , find the intervals where f is concave up and where f is concave down.

Find the relative extrema for .

A rectangle is to have an area of 98 in2. What should be its dimensions if the distance from one corner to the mid-point of a nonadjacent side is to be a minimum?

Answer true or false. f(x) = ln 6x has a point of inflection.

The graph represents a position function. Determine what is happening to the velocity at t = 1.

The graph below depicts the position function of a particle moving on a coordinate line at three different times. For each time specify whether the particle is moving to the left or right (Assume right is the positive direction.) and whether or not it is speeding up or slowing.

Limits and Continuity

The Derivative

Topics in Deifferentiation

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Use a graphing utility to estimate the absolute maximum of f(x) = x⁵ ln x on [1, 5].

f(x) = cos 4x. Find the points of inflection on [0, $\pi$ /2].

The equation, x³ - 2x - 19 = 0 has one real solution for 1 < x < 19. Approximate it by Newton's Method. Use 4.75 for your initial value and calculate eight iterations.

Verify that f(x) = x² + 8 satisfies the hypothesis of the Mean-Value Theorem on the interval [0, 4] and find all values of C that satisfy the conclusion of the theorem.

Use Newton's Method to find the largest positive solution of x⁴ -8x² - 11 = 0.

The largest open interval over which f is concave up for f(x) = 4x³ + 8x² - 7x + 2 is

Use Newton's Method to find the largest positive solution of x⁴ + 5x- 3 = 0.

Find the location of the absolute maximum of 4 tan x on [0, $\pi$ ], if it exists.

Given y = x^2/3(x + 4). Plot any stationary points, inflections points, and cusps which may or may not exist. Approximate answers to 4 decimal places.

Find all relative extrema of f(x) = 7x² - 28x + 2.

The polynomial function x²- 4x + 1 has

Find the point on the curve x² + y² = 36 closest to (0, 8).

Use a graphing utility to generate the graph of f(x) = x⁴ -6x³ + 11x² - 12x + 7, then determine the x-coordinates of all relative extrema on (-10, 10) and identify them as relative maxima or relative minima.

If f(x) = (x -4)⁴ + 7 , find the intervals where f is concave up and where f is concave down.

A rectangle is to have an area of 98 in². What should be its dimensions if the distance from one corner to the mid-point of a nonadjacent side is to be a minimum?