Question 1

The graph represents a position function. Determine what is happening to the velocity at t = 0.

Accepted Answer

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

Question 2

f(x) = 7x4- 2x5 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 3

Use Newton's Method to find the largest positive solution of x4 + x3 -4x -1 = 0.

Accepted Answer

A)  1.5130264 
B)  1.7850245 
C)  1.4011185 
D)  2.2678366 
E)  2.9900000 
A)  1.5130264 
B)  1.7850245 
C)  1.4011185 
D)  2.2678366 
E)  2.9900000

Question 4

If f(x) = sin 2x (0,  $\pi$), find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 5

Find all relative extrema of   .

Accepted Answer

The answer of Find all relative extrema of  ...

Question 6

Given f(x) = 4x3 -5x2 - 7x + 9, find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 7

Let s(t) = 5t6 -4t be a position function. Find v when t = 3.

Accepted Answer

A)  7,290 
B)  1,455 
C)  7,286 
D)  3,633 
E)  4 
A)  7,290 
B)  1,455 
C)  7,286 
D)  3,633 
E)  4

Question 8

Answer true or false. f(x) = x3 -7x2 + 48x + 8 restricted to a domain of [0, 20] has an absolute maximum at x = 2 of 84, and an absolute minimum at x = 8 of 456.

Accepted Answer

A) True 
 B)False

Question 9

If f(x) = x(x + 6)3 , find the inflection points.

Accepted Answer

Question 10

Sketch a continuous curve having the following properties.
f(-4) = 12, f(0) = 6, f(4) = 0, f '(x) > 0 for |x| > 4,
f'(-4) = f '(4) = 0, f '(x)  0 for x > 0.

Accepted Answer

The answer of Sketch a continuous curve having the following...

Question 11

Answer true or false. This can be the graph of a particle's position if the particle is moving to the right at t = 3.3.

Accepted Answer

A) True 
 B)False

Question 12

Given   . Find any stationary and any inflection points.

Accepted Answer

Relative m

Question 13

Find the value of c in the interval [-1, 1] that satisfies the Mean Value Theorem. f(x) = x2 - 6x + 5

Accepted Answer

@#IMG-DLM& = -12
f '

Question 14

The position function of a particle is given by   for t $\ge$ 0. Find the functions for v and a.

Accepted Answer

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

Question 15

Use Newton's Method to find the largest positive solution of x3 + x2 - 4x - 5 = 3. Use 4 for your initial value and calculate eight iterations.

Accepted Answer

A)  3.0769231 
B)  2.5867842 
C)  2.3921405 
D)  2.3307530 
E)  2.3417624 
A)  3.0769231 
B)  2.5867842 
C)  2.3921405 
D)  2.3307530 
E)  2.3417624

Question 16

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x3

Accepted Answer

@#IMG-DLM& = 1 f '(x) = 3x² 3x²

Question 17

Use a graphing utility to estimate the absolute maximum of f(x) = x4 ln x on [1, 3].

Accepted Answer

Question 18

Sketch the graph of y = (x + 4)2/3. Find any stationary points, inflections points, and cusps which may or may not exist.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Relative

Question 19

Sketch the graph of   . Find any stationary points.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Relative

Question 20

If f(x) = (x - 3)4 + 9 , find the location of any inflection points.

Accepted Answer

No inflect

The graph represents a position function. Determine what is happening to the velocity at t = 0.

f(x) = 7x⁴- 2x⁵ , 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 + x³ -4x -1 = 0.

If f(x) = sin 2x (0, $\pi$ ), find the intervals where f is concave up and where f is concave down.

Find all relative extrema of .

Given f(x) = 4x³ -5x² - 7x + 9, find the intervals where f is increasing and where f is decreasing.

Let s(t) = 5t⁶ -4t be a position function. Find v when t = 3.

Answer true or false. f(x) = x³ -7x² + 48x + 8 restricted to a domain of [0, 20] has an absolute maximum at x = 2 of 84, and an absolute minimum at x = 8 of 456.

If f(x) = x(x + 6)³ , find the inflection points.

Sketch a continuous curve having the following properties. f(-4) = 12, f(0) = 6, f(4) = 0, f '(x) > 0 for |x| > 4, f'(-4) = f '(4) = 0, f '(x) < 0 for x < 0, f '(x) > 0 for x > 0.

Answer true or false. This can be the graph of a particle's position if the particle is moving to the right at t = 3.3.

Given . Find any stationary and any inflection points.

Find the value of c in the interval [-1, 1] that satisfies the Mean Value Theorem. f(x) = x² - 6x + 5

The position function of a particle is given by $The position function of a particle is given by for t \ge 0. Find the functions for v and a.$ for t $\ge$ 0. Find the functions for v and a.

Use Newton's Method to find the largest positive solution of x³ + x² - 4x - 5 = 3. Use 4 for your initial value and calculate eight iterations.

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x³

Use a graphing utility to estimate the absolute maximum of f(x) = x⁴ ln x on [1, 3].

Sketch the graph of y = (x + 4)^2/3. Find any stationary points, inflections points, and cusps which may or may not exist.

Sketch the graph of . Find any stationary points.

If f(x) = (x - 3)⁴ + 9 , find the location of any inflection points.

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

The graph represents a position function. Determine what is happening to the velocity at t = 0.

f(x) = 7x4- 2x5 , 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 + x3 -4x -1 = 0.

If f(x) = sin 2x (0, π\piπ ), find the intervals where f is concave up and where f is concave down.

Find all relative extrema of .

Given f(x) = 4x3 -5x2 - 7x + 9, find the intervals where f is increasing and where f is decreasing.

Let s(t) = 5t6 -4t be a position function. Find v when t = 3.

Answer true or false. f(x) = x3 -7x2 + 48x + 8 restricted to a domain of [0, 20] has an absolute maximum at x = 2 of 84, and an absolute minimum at x = 8 of 456.

If f(x) = x(x + 6)3 , find the inflection points.

Sketch a continuous curve having the following properties. f(-4) = 12, f(0) = 6, f(4) = 0, f '(x) > 0 for |x| > 4, f'(-4) = f '(4) = 0, f '(x) < 0 for x < 0, f '(x) > 0 for x > 0.

Answer true or false. This can be the graph of a particle's position if the particle is moving to the right at t = 3.3.

Given . Find any stationary and any inflection points.

Find the value of c in the interval [-1, 1] that satisfies the Mean Value Theorem. f(x) = x2 - 6x + 5

The position function of a particle is given by for t ≥\ge≥ 0. Find the functions for v and a.

Use Newton's Method to find the largest positive solution of x3 + x2 - 4x - 5 = 3. Use 4 for your initial value and calculate eight iterations.

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x3

Use a graphing utility to estimate the absolute maximum of f(x) = x4 ln x on [1, 3].

Sketch the graph of y = (x + 4)2/3. Find any stationary points, inflections points, and cusps which may or may not exist.

Sketch the graph of . Find any stationary points.

If f(x) = (x - 3)4 + 9 , find the location of any inflection points.

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

f(x) = 7x⁴- 2x⁵ , 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 + x³ -4x -1 = 0.

If f(x) = sin 2x (0, $\pi$ ), find the intervals where f is concave up and where f is concave down.

Given f(x) = 4x³ -5x² - 7x + 9, find the intervals where f is increasing and where f is decreasing.

Let s(t) = 5t⁶ -4t be a position function. Find v when t = 3.

Answer true or false. f(x) = x³ -7x² + 48x + 8 restricted to a domain of [0, 20] has an absolute maximum at x = 2 of 84, and an absolute minimum at x = 8 of 456.

If f(x) = x(x + 6)³ , find the inflection points.

Find the value of c in the interval [-1, 1] that satisfies the Mean Value Theorem. f(x) = x² - 6x + 5

The position function of a particle is given by $The position function of a particle is given by for t \ge 0. Find the functions for v and a.$ for t $\ge$ 0. Find the functions for v and a.

Use Newton's Method to find the largest positive solution of x³ + x² - 4x - 5 = 3. Use 4 for your initial value and calculate eight iterations.

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x³

Use a graphing utility to estimate the absolute maximum of f(x) = x⁴ ln x on [1, 3].

Sketch the graph of y = (x + 4)^2/3. Find any stationary points, inflections points, and cusps which may or may not exist.

If f(x) = (x - 3)⁴ + 9 , find the location of any inflection points.