Question 1

f(x) = |4 -2x| has an absolute minimum of

Accepted Answer

A)  4 
B)  2 
C)  -4 
D)  -8 
E)  0 
A)  4 
B)  2 
C)  -4 
D)  -8 
E)  0

Question 2

Find the relative extreme values for f(x) = 1 -x2/5 on the interval [-1, 1] and determine where those values occur.

Accepted Answer

@#IMG-DLM& ; f '(x) does not exist at x

Question 3

Answer true or false. Rolle's Theorem is used to find the zeros of a function.

Accepted Answer

A) True 
 B)False

Question 4

Answer true or false. A graphing utility can be used to show f(x) = |x3| has a relative maximum.

Accepted Answer

A) True 
 B)False

Question 5

Answer true or false. The point on the parabola y = 6x2 closest to (0, 0.8) is (0, 0).

Accepted Answer

A) True 
 B)False

Question 6

Use a graphing utility to determine where   is decreasing on [0, 2 $\pi$].

Accepted Answer

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

Question 7

If f(x) = x(x -13)5 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 8

Answer true or false. f(x) = 4x5 - 2x2 + 11 has an absolute maximum and an absolute minimum.

Accepted Answer

A) True 
 B)False

Question 9

Use a graphing utility to estimate the absolute maximum of f(x) = -(ln x)8 on [1, 10].

Accepted Answer

Question 10

If f(x) = x(x - 6)2 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 11

The position function of a particle is given by s(t) = 7t - 23. Find the velocity function.

Accepted Answer

The answer of The position function of a particle is...

Question 12

Answer true or false. The rectangle with the largest area that can be drawn inside a circle is a square.

Accepted Answer

A) True 
 B)False

Question 13

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 righ

Question 14

Use Newton's Method to find the largest positive solution of x4 + 4x3 -2x2 - 9x - 2 = 0. Use 4 for your initial value and calculate eight iterations.

Accepted Answer

A)  1.6033441 
B)  1.5530570 
C)  1.8062561 
D)  2.2423497 
E)  2.9550827 
A)  1.6033441 
B)  1.5530570 
C)  1.8062561 
D)  2.2423497 
E)  2.9550827

Question 15

Find the point on the curve x2 + y2 = 121 closest to (0, 12).

Accepted Answer

Question 16

Approximate   by applying Newton's Method to the equation x2 -10 = 0.

Accepted Answer

A)  3.1622777 
B)  3.1621577 
C)  3.1622657 
D)  3.162281 
E)  3.166667 
A)  3.1622777 
B)  3.1621577 
C)  3.1622657 
D)  3.162281 
E)  3.166667

Question 17

Answer true or false.   has an oblique asymptote.

Accepted Answer

A) True 
 B)False

Question 18

Use a graphing utility to estimate the absolute minimum of f(x) = ln(x8) on [1, 3].

Accepted Answer

Question 19

Sketch the graph of   . Find any stationary points and any points of inflection. Also find any horizontal and vertical asymptotes.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Relative minimum a

Question 20

Use Newton's Method to find the x-coordinate of the intersection of y = x4 + 2x3 and y = 2x2 + 6x + 3. Use 3 for your initial value and calculate eight iterations.

Accepted Answer

A)  2.3333333 
B)  1.9347826 
C)  1.7649117 
D)  1.7331057 
E)  1.7320508 
A)  2.3333333 
B)  1.9347826 
C)  1.7649117 
D)  1.7331057 
E)  1.7320508

f(x) = |4 -2x| has an absolute minimum of

Find the relative extreme values for f(x) = 1 -x^2/5 on the interval [-1, 1] and determine where those values occur.

Answer true or false. Rolle's Theorem is used to find the zeros of a function.

Answer true or false. A graphing utility can be used to show f(x) = |x³| has a relative maximum.

Answer true or false. The point on the parabola y = 6x² closest to (0, 0.8) is (0, 0).

Use a graphing utility to determine where $Use a graphing utility to determine where is decreasing on [0, 2 \pi ].$ is decreasing on [0, 2 $\pi$ ].

If f(x) = x(x -13)⁵ , find the intervals where f is increasing and where f is decreasing.

Answer true or false. f(x) = 4x⁵ - 2x² + 11 has an absolute maximum and an absolute minimum.

Use a graphing utility to estimate the absolute maximum of f(x) = -(ln x)⁸ on [1, 10].

If f(x) = x(x - 6)² , find the intervals where f is concave up and where f is concave down.

The position function of a particle is given by s(t) = 7t - 23. Find the velocity function.

Answer true or false. The rectangle with the largest area that can be drawn inside a circle is a square.

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.

Use Newton's Method to find the largest positive solution of x⁴ + 4x³ -2x² - 9x - 2 = 0. Use 4 for your initial value and calculate eight iterations.

Find the point on the curve x² + y² = 121 closest to (0, 12).

Approximate by applying Newton's Method to the equation x² -10 = 0.

Answer true or false. has an oblique asymptote.

Use a graphing utility to estimate the absolute minimum of f(x) = ln(x⁸) on [1, 3].

Sketch the graph of . Find any stationary points and any points of inflection. Also find any horizontal and vertical asymptotes.

Use Newton's Method to find the x-coordinate of the intersection of y = x⁴ + 2x³ and y = 2x² + 6x + 3. Use 3 for your initial value and calculate eight iterations.

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

f(x) = |4 -2x| has an absolute minimum of

Find the relative extreme values for f(x) = 1 -x2/5 on the interval [-1, 1] and determine where those values occur.

Answer true or false. Rolle's Theorem is used to find the zeros of a function.

Answer true or false. A graphing utility can be used to show f(x) = |x3| has a relative maximum.

Answer true or false. The point on the parabola y = 6x2 closest to (0, 0.8) is (0, 0).

Use a graphing utility to determine where is decreasing on [0, 2 π\piπ ].

If f(x) = x(x -13)5 , find the intervals where f is increasing and where f is decreasing.

Answer true or false. f(x) = 4x5 - 2x2 + 11 has an absolute maximum and an absolute minimum.

Use a graphing utility to estimate the absolute maximum of f(x) = -(ln x)8 on [1, 10].

If f(x) = x(x - 6)2 , find the intervals where f is concave up and where f is concave down.

The position function of a particle is given by s(t) = 7t - 23. Find the velocity function.

Answer true or false. The rectangle with the largest area that can be drawn inside a circle is a square.

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.

Use Newton's Method to find the largest positive solution of x4 + 4x3 -2x2 - 9x - 2 = 0. Use 4 for your initial value and calculate eight iterations.

Find the point on the curve x2 + y2 = 121 closest to (0, 12).

Approximate by applying Newton's Method to the equation x2 -10 = 0.

Answer true or false. has an oblique asymptote.

Use a graphing utility to estimate the absolute minimum of f(x) = ln(x8) on [1, 3].

Sketch the graph of . Find any stationary points and any points of inflection. Also find any horizontal and vertical asymptotes.

Use Newton's Method to find the x-coordinate of the intersection of y = x4 + 2x3 and y = 2x2 + 6x + 3. Use 3 for your initial value and calculate eight iterations.

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

Find the relative extreme values for f(x) = 1 -x^2/5 on the interval [-1, 1] and determine where those values occur.

Answer true or false. A graphing utility can be used to show f(x) = |x³| has a relative maximum.

Answer true or false. The point on the parabola y = 6x² closest to (0, 0.8) is (0, 0).

Use a graphing utility to determine where $Use a graphing utility to determine where is decreasing on [0, 2 \pi ].$ is decreasing on [0, 2 $\pi$ ].

If f(x) = x(x -13)⁵ , find the intervals where f is increasing and where f is decreasing.

Answer true or false. f(x) = 4x⁵ - 2x² + 11 has an absolute maximum and an absolute minimum.

Use a graphing utility to estimate the absolute maximum of f(x) = -(ln x)⁸ on [1, 10].

If f(x) = x(x - 6)² , find the intervals where f is concave up and where f is concave down.

Use Newton's Method to find the largest positive solution of x⁴ + 4x³ -2x² - 9x - 2 = 0. Use 4 for your initial value and calculate eight iterations.

Find the point on the curve x² + y² = 121 closest to (0, 12).

Approximate by applying Newton's Method to the equation x² -10 = 0.

Use a graphing utility to estimate the absolute minimum of f(x) = ln(x⁸) on [1, 3].

Use Newton's Method to find the x-coordinate of the intersection of y = x⁴ + 2x³ and y = 2x² + 6x + 3. Use 3 for your initial value and calculate eight iterations.