Question 1

Find the extreme values for   on the interval [0, 2] and determine where those values occur.

Accepted Answer

@#IMG-DLM& ; f '(x) = 0 when x = -1 and

Question 2

Find the extreme values for   on the interval [0, 50] and determine where those occur.

Accepted Answer

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

Question 3

Use Newton's Method to find the largest positive solution of x4 + x3 - 2x2- 5x -7 = 0. Use 4 for your initial value and calculate eight iterations.

Accepted Answer

A)  3.0777385 
B)  2.4705751 
C)  2.0313608 
D)  2.1446813 
E)  2.0413802 
A)  3.0777385 
B)  2.4705751 
C)  2.0313608 
D)  2.1446813 
E)  2.0413802

Question 4

Find the relative extrema for   .

Accepted Answer

@#IMG-DLM& Critical points at x = -1 and

Question 5

Answer true or false. f(x) = 6e-x has no relative minimum.

Accepted Answer

A) True 
 B)False

Question 6

Answer true or false.   has a relative maximum on (0, $\infty$).

Accepted Answer

A) True 
 B)False

Question 7

Answer true or false. All relative extrema occur at critical points.

Accepted Answer

A) True 
 B)False

Question 8

Find the relative extreme values for f(x) = 2x3 - 9x2 + 12x + 5 on the interval [-10, 10] and determine where those values occur.

Accepted Answer

f '(x) = 6x² - 18x + 12 = (3x

Question 9

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 10

Find the value c that satisfies Rolle's Theorem for f(x) = 9 cos 6x on   .

Accepted Answer

A)    
B)    
C)  0 
D)    
E)    
A)    
B)    
C)  0 
D)    
E)

Question 11

Find the relative extreme values for f(x) = 1 -x2/7 on the interval [-1, 1] and determine where those values occur.

Accepted Answer

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

Question 12

Find the point on the curve x2 + y2 = 25 closest to (0, 9).

Accepted Answer

A)  (0, 25) 
B)  (0, 5) 
C)  (0, 9) 
D)  (5, 0) 
E)  (25, 0) 
A)  (0, 25) 
B)  (0, 5) 
C)  (0, 9) 
D)  (5, 0) 
E)  (25, 0)

Question 13

Answer true or false. All relative extrema occur at critical points.

Accepted Answer

A) True 
 B)False

Question 14

f(x) = 6 sin 5x. Find the points of inflection on [0, 2 $\pi$/5].

Accepted Answer

The answer of f(x) = 6 sin 5x. Find the...

Question 15

The function f(x) = x7 -8 has a point of inflection with an x-coordinate of

Accepted Answer

A)  8 
B)  -8 
C)  7 
D)  0 
E)  None exist 
A)  8 
B)  -8 
C)  7 
D)  0 
E)  None exist

Question 16

If f(x) = ax4 - bx2, find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing on (-

@#IMG-DLM&

Question 17

The position function of a particle is given by s(t) = 7t3 - 4t. Find the velocity function.

Accepted Answer

v(t) = 21t

Question 18

The position function of a particle is given by s = 5t3 - 9t2 + 6t + 7 for t $\ge$ 0. Find the functions for v and a.

Accepted Answer

v = 15t<su

Question 19

A right triangle has a perimeter of 56. What are the lengths of each side if the area contained within the triangle is to be maximized?

Accepted Answer

A)    ,
  ,
  
B)  24, 24, 8 
C)    ,
  ,
  
D)    ,
  ,
  
E)  21, 21, 14 
A)    ,
  ,
  
B)  24, 24, 8 
C)    ,
  ,
  
D)    ,
  ,
  
E)  21, 21, 14

Question 20

Find the relative extrema for   .

Accepted Answer

@#IMG-DLM& Critical points at x = -1 and

Find the extreme values for on the interval [0, 2] and determine where those values occur.

Find the extreme values for on the interval [0, 50] and determine where those occur.

Use Newton's Method to find the largest positive solution of x⁴ + x³ - 2x²- 5x -7 = 0. Use 4 for your initial value and calculate eight iterations.

Find the relative extrema for .

Answer true or false. f(x) = 6e^-^x has no relative minimum.

Answer true or false. $Answer true or false. has a relative maximum on (0, \infty ).$ has a relative maximum on (0, $\infty$ ).

Answer true or false. All relative extrema occur at critical points.

Find the relative extreme values for f(x) = 2x³ - 9x² + 12x + 5 on the interval [-10, 10] and determine where those values occur.

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

Find the value c that satisfies Rolle's Theorem for f(x) = 9 cos 6x on .

Find the relative extreme values for f(x) = 1 -x^2/7 on the interval [-1, 1] and determine where those values occur.

Find the point on the curve x² + y² = 25 closest to (0, 9).

Answer true or false. All relative extrema occur at critical points.

f(x) = 6 sin 5x. Find the points of inflection on [0, 2 $\pi$ /5].

The function f(x) = x⁷ -8 has a point of inflection with an x-coordinate of

If f(x) = ax⁴ - bx², find the intervals where f is increasing and where f is decreasing.

The position function of a particle is given by s(t) = 7t³ - 4t. Find the velocity function.

The position function of a particle is given by s = 5t³ - 9t² + 6t + 7 for t $\ge$ 0. Find the functions for v and a.

A right triangle has a perimeter of 56. What are the lengths of each side if the area contained within the triangle is to be maximized?

Find the relative extrema for .

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

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Exam 4: The Derivative in Graphing and Applications

Find the extreme values for on the interval [0, 2] and determine where those values occur.

Find the extreme values for on the interval [0, 50] and determine where those occur.

Use Newton's Method to find the largest positive solution of x4 + x3 - 2x2- 5x -7 = 0. Use 4 for your initial value and calculate eight iterations.

Find the relative extrema for .

Answer true or false. f(x) = 6e-x has no relative minimum.

Answer true or false. has a relative maximum on (0, ∞\infty∞ ).

Answer true or false. All relative extrema occur at critical points.

Find the relative extreme values for f(x) = 2x3 - 9x2 + 12x + 5 on the interval [-10, 10] and determine where those values occur.

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

Find the value c that satisfies Rolle's Theorem for f(x) = 9 cos 6x on .

Find the relative extreme values for f(x) = 1 -x2/7 on the interval [-1, 1] and determine where those values occur.

Find the point on the curve x2 + y2 = 25 closest to (0, 9).

Answer true or false. All relative extrema occur at critical points.

f(x) = 6 sin 5x. Find the points of inflection on [0, 2 π\piπ /5].

The function f(x) = x7 -8 has a point of inflection with an x-coordinate of

If f(x) = ax4 - bx2, find the intervals where f is increasing and where f is decreasing.

The position function of a particle is given by s(t) = 7t3 - 4t. Find the velocity function.

The position function of a particle is given by s = 5t3 - 9t2 + 6t + 7 for t ≥\ge≥ 0. Find the functions for v and a.

A right triangle has a perimeter of 56. What are the lengths of each side if the area contained within the triangle is to be maximized?

Find the relative extrema for .

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 Newton's Method to find the largest positive solution of x⁴ + x³ - 2x²- 5x -7 = 0. Use 4 for your initial value and calculate eight iterations.

Answer true or false. f(x) = 6e^-^x has no relative minimum.

Answer true or false. $Answer true or false. has a relative maximum on (0, \infty ).$ has a relative maximum on (0, $\infty$ ).

Find the relative extreme values for f(x) = 2x³ - 9x² + 12x + 5 on the interval [-10, 10] and determine where those values occur.

Find the relative extreme values for f(x) = 1 -x^2/7 on the interval [-1, 1] and determine where those values occur.

Find the point on the curve x² + y² = 25 closest to (0, 9).

f(x) = 6 sin 5x. Find the points of inflection on [0, 2 $\pi$ /5].

The function f(x) = x⁷ -8 has a point of inflection with an x-coordinate of

If f(x) = ax⁴ - bx², find the intervals where f is increasing and where f is decreasing.

The position function of a particle is given by s(t) = 7t³ - 4t. Find the velocity function.

The position function of a particle is given by s = 5t³ - 9t² + 6t + 7 for t $\ge$ 0. Find the functions for v and a.