Question 1

Find the value c that satisfies Rolle's Theorem for f(x) = 9 cos 3x on   .

Accepted Answer

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

Question 2

Given f(x) = cos2x + sin x . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval   .

Accepted Answer

Absolute minimum of

Question 3

The position function of a particle is given by s(t) = 7t5 - 3t. Find the velocity function.

Accepted Answer

v(t) = 35t

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

Use a graphing utility to estimate the absolute maximum of   on [-2, 2].

Accepted Answer

The answer of Use a graphing utility to estimate the...

Question 6

Find the relative extrema for f(x) = 4x2 - 8x + 3.

Accepted Answer

f '(x) = 8x - 8
Critical point

Question 7

Sketch the graph of   . Find all oblique asymptotes.

Accepted Answer

@#IMG-DLM& so y = x

Question 8

Find the relative extrema for f(x) = 3x + 3x4/5.

Accepted Answer

Critical points at @#IMG-DLM&

Question 9

Approximate   by applying Newton's Method to the equation x4 - 34 = 0.

Accepted Answer

f(x) = x⁴ - 34 f '(x) = 4x

Question 10

Use Rolle's Theorem to show that f(x) = x3 + ax + b, where a > 0, cannot have more than one real root.

Accepted Answer

Suppose f has more than one real root. L

Question 11

Answer true or false. According to Rolle's Theorem if a function's derivative is 0, the graph of the function must cross the y-axis.

Accepted Answer

A) True 
 B)False

Question 12

The rational function   has

Accepted Answer

A)  a stationary point at x = 1 
B)  a stationary point at x = -1 
C)  two stationary points at approximately x = -1.732 and x = 1.732 
D)  three stationary points approximately at x = 0, x = -1.732 and x = 1.732 
E)  no stationary points 
A)  a stationary point at x = 1 
B)  a stationary point at x = -1 
C)  two stationary points at approximately x = -1.732 and x = 1.732 
D)  three stationary points approximately at x = 0, x = -1.732 and x = 1.732 
E)  no stationary points

Question 13

A can containing 16 in3 of tuna and water is to be made in the form of a circular cylinder. What dimensions of the can will require the least amount of material? (V =  $\pi$r2h, S = 2 $\pi$rh, A =  $\pi$r2)

Accepted Answer

V = @#LAT-DLM&r²h = 16, so @#IMG-DLM&

Question 14

f(x) = x2 + 4x + 1 has a

Accepted Answer

A)  relative maximum at x = -2 
B)  relative minimum at x = -2 
C)  relative maximum at x = -4 
D)  relative minimum at x = -4 
E)  relative maximum at x = -1 
A)  relative maximum at x = -2 
B)  relative minimum at x = -2 
C)  relative maximum at x = -4 
D)  relative minimum at x = -4 
E)  relative maximum at x = -1

Question 15

Given   . Find all vertical, horizontal and oblique asymptotes.

Accepted Answer

@#IMG-DLM& so there is a verti

Question 16

f(x) = 9x4 - 8x5 , find the location of any inflection points.

Accepted Answer

The answer of f(x) = 9x4 - 8x5 , find...

Question 17

The graph represents a position function. Determine what is happening to the velocity at t = 5.

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 18

Find the value c such that the conclusion of Rolle's Theorem are satisfied for f(x) = 2x2 - 2 on [-3, 3].

Accepted Answer

A)  0 
B)  -1 
C)  1 
D)  0.5 
E)  -0.5 
A)  0 
B)  -1 
C)  1 
D)  0.5 
E)  -0.5

Question 19

Find the value c that satisfies Rolle's Theorem for f(x) = x3 -4x on [-2, 2].

Accepted Answer

A)  -2.0 
B)  1.2 
C)  2.0 
D)  4.0 
E)  -4.0 
A)  -2.0 
B)  1.2 
C)  2.0 
D)  4.0 
E)  -4.0

Question 20

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

Accepted Answer

The answer of f(x) = 2 sin 4x. Find the...

Find the value c that satisfies Rolle's Theorem for f(x) = 9 cos 3x on .

Given f(x) = cos²x + sin x . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval .

The position function of a particle is given by s(t) = 7t⁵ - 3t. Find the velocity function.

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

Use a graphing utility to estimate the absolute maximum of on [-2, 2].

Find the relative extrema for f(x) = 4x² - 8x + 3.

Sketch the graph of . Find all oblique asymptotes.

Find the relative extrema for f(x) = 3x + 3x⁴^/⁵.

Approximate by applying Newton's Method to the equation x⁴ - 34 = 0.

Use Rolle's Theorem to show that f(x) = x³ + ax + b, where a > 0, cannot have more than one real root.

Answer true or false. According to Rolle's Theorem if a function's derivative is 0, the graph of the function must cross the y-axis.

The rational function has

A can containing 16 in³ of tuna and water is to be made in the form of a circular cylinder. What dimensions of the can will require the least amount of material? (V = $\pi$ r²h, S = 2 $\pi$ rh, A = $\pi$ r²)

f(x) = x² + 4x + 1 has a

Given . Find all vertical, horizontal and oblique asymptotes.

f(x) = 9x⁴ - 8x⁵ , find the location of any inflection points.

The graph represents a position function. Determine what is happening to the velocity at t = 5.

Find the value c such that the conclusion of Rolle's Theorem are satisfied for f(x) = 2x² - 2 on [-3, 3].

Find the value c that satisfies Rolle's Theorem for f(x) = x³ -4x on [-2, 2].

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

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 value c that satisfies Rolle's Theorem for f(x) = 9 cos 3x on .

Given f(x) = cos2x + sin x . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval .

The position function of a particle is given by s(t) = 7t5 - 3t. Find the velocity function.

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

Use a graphing utility to estimate the absolute maximum of on [-2, 2].

Find the relative extrema for f(x) = 4x2 - 8x + 3.

Sketch the graph of . Find all oblique asymptotes.

Find the relative extrema for f(x) = 3x + 3x4/5.

Approximate by applying Newton's Method to the equation x4 - 34 = 0.

Use Rolle's Theorem to show that f(x) = x3 + ax + b, where a > 0, cannot have more than one real root.

Answer true or false. According to Rolle's Theorem if a function's derivative is 0, the graph of the function must cross the y-axis.

The rational function has

A can containing 16 in3 of tuna and water is to be made in the form of a circular cylinder. What dimensions of the can will require the least amount of material? (V = π\piπ r2h, S = 2 π\piπ rh, A = π\piπ r2)

f(x) = x2 + 4x + 1 has a

Given . Find all vertical, horizontal and oblique asymptotes.

f(x) = 9x4 - 8x5 , find the location of any inflection points.

The graph represents a position function. Determine what is happening to the velocity at t = 5.

Find the value c such that the conclusion of Rolle's Theorem are satisfied for f(x) = 2x2 - 2 on [-3, 3].

Find the value c that satisfies Rolle's Theorem for f(x) = x3 -4x on [-2, 2].

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

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

Given f(x) = cos²x + sin x . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval .

The position function of a particle is given by s(t) = 7t⁵ - 3t. Find the velocity function.

Find the relative extrema for f(x) = 4x² - 8x + 3.

Find the relative extrema for f(x) = 3x + 3x⁴^/⁵.

Approximate by applying Newton's Method to the equation x⁴ - 34 = 0.

Use Rolle's Theorem to show that f(x) = x³ + ax + b, where a > 0, cannot have more than one real root.

A can containing 16 in³ of tuna and water is to be made in the form of a circular cylinder. What dimensions of the can will require the least amount of material? (V = $\pi$ r²h, S = 2 $\pi$ rh, A = $\pi$ r²)

f(x) = x² + 4x + 1 has a

f(x) = 9x⁴ - 8x⁵ , find the location of any inflection points.

Find the value c such that the conclusion of Rolle's Theorem are satisfied for f(x) = 2x² - 2 on [-3, 3].

Find the value c that satisfies Rolle's Theorem for f(x) = x³ -4x on [-2, 2].

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