Question 1

Find the relative extrema for f(x) = 5x + cos 2x, 0 < x <  $\pi$.

Accepted Answer

f '(x) = 5 - 2 sin 2x
Critical points at

Question 2

s(t) = 5t-4t3, t $\ge$0. The acceleration function is

Accepted Answer

A)  5 - 8t 
B)  8t 
C)  5 - 8t2 
D)  24t 
E)  5t - 4t 
A)  5 - 8t 
B)  8t 
C)  5 - 8t2 
D)  24t 
E)  5t - 4t

Question 3

If f(x) = 6x4- 16x3 + 11 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 4

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

Accepted Answer

Increasing

Question 5

Find the relative extrema for   .

Accepted Answer

Relative m

Question 6

The position function of a particle is given by s = 7t2 - 4t + 5 for t $\ge$ 0. Find the functions for v and a.

Accepted Answer

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

Question 7

Given y = x1/3(x + 6). Find any stationary points and any inflections points.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Relative minimum at (-1.5, -

Question 8

Find the relative extrema for f(x) = 2x + 2x2/3.

Accepted Answer

Critical points at @#IMG-DLM&

Question 9

Find the extreme values for   on the interval [0, 100] and determine where those occur.

Accepted Answer

@#IMG-DLM& , so there are no c

Question 10

If f(x) = 12x4 -6x3 + 2 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 11

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 5y = 25-x2. Find the area of the largest such triangle.

Accepted Answer

The answer of An isosceles triangle is drawn with its...

Question 12

Sketch the graph of y = x3 -6x2 + 9x + 4. Find any stationary points and any points of inflection.

Accepted Answer

ly' = 3x² - 12x + 9

Question 13

If f(x) = (x - 9)4 + 9 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

The answer of If f(x) = (x - 9)4 +...

Question 14

Does   satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 16]? If so, find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

Yes, since f is continuous ove

Question 15

s(t) = 4t - 8t2, t $\ge$ 0. The velocity function is

Accepted Answer

A)  4 - 8t 
B)  4t - 16t2 
C)  4 - 16t 
D)  8 - 16t 
E)  4t - 8t 
A)  4 - 8t 
B)  4t - 16t2 
C)  4 - 16t 
D)  8 - 16t 
E)  4t - 8t

Question 16

Answer true or false. If f(x) has an absolute minimum at x = 7, -f(x) also has an absolute minimum at x = 7.

Accepted Answer

A) True 
 B)False

Question 17

Given f(x) = 4x3 -3x2 - 8x + 1, find the coordinate of the inflection point.

Accepted Answer

The answer of Given f(x) = 4x3 -3x2 - 8x...

Question 18

Answer true or false. If f ''(-9) = -6 and f''(9) = 6, then there must be a point of inflection on (-9, 9).

Accepted Answer

A) True 
 B)False

Question 19

Use Newton's Method to find the largest positive solution of x4 -4x2 -1 = 0.

Accepted Answer

A)  2.1963970 
B)  2.5077099 
C)  2.0581710 
D)  3.0502422 
E)  3.8608696 
A)  2.1963970 
B)  2.5077099 
C)  2.0581710 
D)  3.0502422 
E)  3.8608696

Question 20

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

Accepted Answer

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

Find the relative extrema for f(x) = 5x + cos 2x, 0 < x < $\pi$ .

s(t) = 5t-4t³, t $\ge$ 0. The acceleration function is

If f(x) = 6x⁴- 16x³ + 11 , find the intervals where f is increasing and where f is decreasing.

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

Find the relative extrema for .

The position function of a particle is given by s = 7t² - 4t + 5 for t $\ge$ 0. Find the functions for v and a.

Given y = x^1/3(x + 6). Find any stationary points and any inflections points.

Find the relative extrema for f(x) = 2x + 2x²^/³.

Find the extreme values for on the interval [0, 100] and determine where those occur.

If f(x) = 12x⁴ -6x³ + 2 , find the intervals where f is concave up and where f is concave down.

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 5y = 25-x². Find the area of the largest such triangle.

Sketch the graph of y = x³ -6x² + 9x + 4. Find any stationary points and any points of inflection.

If f(x) = (x - 9)⁴ + 9 , find the intervals where f is concave up and where f is concave down.

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 16]? If so, find all values of C that satisfy the conclusion of the theorem.

s(t) = 4t - 8t², t $\ge$ 0. The velocity function is

Answer true or false. If f(x) has an absolute minimum at x = 7, -f(x) also has an absolute minimum at x = 7.

Given f(x) = 4x³ -3x² - 8x + 1, find the coordinate of the inflection point.

Answer true or false. If f ''(-9) = -6 and f''(9) = 6, then there must be a point of inflection on (-9, 9).

Use Newton's Method to find the largest positive solution of x⁴ -4x² -1 = 0.

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

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

Find the relative extrema for f(x) = 5x + cos 2x, 0 < x < π\piπ .

s(t) = 5t-4t3, t ≥\ge≥ 0. The acceleration function is

If f(x) = 6x4- 16x3 + 11 , find the intervals where f is increasing and where f is decreasing.

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

Find the relative extrema for .

The position function of a particle is given by s = 7t2 - 4t + 5 for t ≥\ge≥ 0. Find the functions for v and a.

Given y = x1/3(x + 6). Find any stationary points and any inflections points.

Find the relative extrema for f(x) = 2x + 2x2/3.

Find the extreme values for on the interval [0, 100] and determine where those occur.

If f(x) = 12x4 -6x3 + 2 , find the intervals where f is concave up and where f is concave down.

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 5y = 25-x2. Find the area of the largest such triangle.

Sketch the graph of y = x3 -6x2 + 9x + 4. Find any stationary points and any points of inflection.

If f(x) = (x - 9)4 + 9 , find the intervals where f is concave up and where f is concave down.

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 16]? If so, find all values of C that satisfy the conclusion of the theorem.

s(t) = 4t - 8t2, t ≥\ge≥ 0. The velocity function is

Answer true or false. If f(x) has an absolute minimum at x = 7, -f(x) also has an absolute minimum at x = 7.

Given f(x) = 4x3 -3x2 - 8x + 1, find the coordinate of the inflection point.

Answer true or false. If f ''(-9) = -6 and f''(9) = 6, then there must be a point of inflection on (-9, 9).

Use Newton's Method to find the largest positive solution of x4 -4x2 -1 = 0.

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

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 extrema for f(x) = 5x + cos 2x, 0 < x < $\pi$ .

s(t) = 5t-4t³, t $\ge$ 0. The acceleration function is

If f(x) = 6x⁴- 16x³ + 11 , find the intervals where f is increasing and where f is decreasing.

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

The position function of a particle is given by s = 7t² - 4t + 5 for t $\ge$ 0. Find the functions for v and a.

Given y = x^1/3(x + 6). Find any stationary points and any inflections points.

Find the relative extrema for f(x) = 2x + 2x²^/³.

If f(x) = 12x⁴ -6x³ + 2 , find the intervals where f is concave up and where f is concave down.

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 5y = 25-x². Find the area of the largest such triangle.

Sketch the graph of y = x³ -6x² + 9x + 4. Find any stationary points and any points of inflection.

If f(x) = (x - 9)⁴ + 9 , find the intervals where f is concave up and where f is concave down.

s(t) = 4t - 8t², t $\ge$ 0. The velocity function is

Given f(x) = 4x³ -3x² - 8x + 1, find the coordinate of the inflection point.

Use Newton's Method to find the largest positive solution of x⁴ -4x² -1 = 0.