Question 1

Answer true or false. f(x) = e6x has a horizontal asymptote at y = 0.

Accepted Answer

A) True 
 B)False

Question 2

If f(x) = x4 - 12x2 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 3

Verify that f(x) = x2 + 3x -1 satisfies the hypothesis of the Mean-Value Theorem over the interval [0, 1] and find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

f(0) = -1
f(1) = 3
f

Question 4

An open cylindrical trash can is to hold 19 cubic feet of material. What should be its dimensions if the cost of material used is to be a minimum? [Surface Area, S = $\pi$r2 + 2 $\pi$rh where r = radius and h = height.]

Accepted Answer

Let r be the radius of the can

Question 5

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 6

Answer true or false. A graphing utility can be used to show f(x) = |4x2| - 6 has two relative maxima on [-10, 10].

Accepted Answer

A) True 
 B)False

Question 7

Find the point on the curve x2 + y2 = 64 closest to (7, 0).

Accepted Answer

Question 8

The position function of a particle is given by s = t3 - 6t2 - 8t for t $\ge$ 0. Find the functions for v and a.

Accepted Answer

v = 3t<sup

Question 9

Answer true or false. If f ''(-2) = -4 and f ''(2) = 4, then there must be an inflection point on (-2, 2).

Accepted Answer

A) True 
 B)False

Question 10

Answer true or false. The triangle with the largest area that can be drawn inside a circle is an equilateral triangle.

Accepted Answer

A) True 
 B)False

Question 11

Use a graphing utility to estimate the absolute minimum of f(x) = e x (ln x)6 on [1, 5].

Accepted Answer

Question 12

Sketch a continuous curve having the following properties.
f(-5) = 10, f(0) = 5, f(5) = 0, f'(x) > 0 for |x| > 5,
f'(-5) = f'(5) = 0, f'(x)  0 for x > 0.

Accepted Answer

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

Question 13

Find the relative extrema for f(x) = 3x + cos 2x, 0 < x <  $\pi$.

Accepted Answer

f '(x) = 3 - 2 sin 2x
Critical points at

Question 14

Sketch a continuous curve having the following properties.
f(0) = 1, f(-1) = f(1) = 0; f '(x) > 0 for (-$\infty$,0) and f '(x) < 0 for (0, +$\infty$), f'(x) < 0 for (-$\infty$, +$\infty$).

Accepted Answer

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

Question 15

Answer true or false. A graphing utility can be used to show f(x) = |3x2| - 12 has two relative maxima on [-20, 20].

Accepted Answer

A) True 
 B)False

Question 16

f(x) = |x - 8| has

Accepted Answer

A)  a relative minimum at x = 0 
B)  a relative maximum at x = 0 
C)  a relative maximum at x = 8 
D)  a relative minimum at x = 8 
E)  a relative minimum at x = -8 
A)  a relative minimum at x = 0 
B)  a relative maximum at x = 0 
C)  a relative maximum at x = 8 
D)  a relative minimum at x = 8 
E)  a relative minimum at x = -8

Question 17

Find the dimensions of the rectangular area of maximum area which can be laid out within a triangle of base 16 and altitude 4 if one side of the rectangle lies on the base of the triangle.

Accepted Answer

Let x and y be as shown in the

Question 18

A rancher is going to build a 3-sided cattle enclosure with a divider down the middle as shown to the right. The cost per foot of the 3 side walls will be $4/foot, while the back wall, being taller, will be $8/foot. If the rancher wishes to enclose an area of 384 ft2, what dimensions of the enclosure will minimize his cost?

Accepted Answer

The area of the enclosure is A

Question 19

Answer true or false. The Mean-Value Theorem guarantees there is at least one c on [0, 1] such that f '(x) = 0.8 when f(x) = x.

Accepted Answer

A) True 
 B)False

Question 20

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

Accepted Answer

@#IMG-DLM& @#IMG-DLM& No relative minima

Answer true or false. f(x) = e⁶^x has a horizontal asymptote at y = 0.

If f(x) = x⁴ - 12x²_,find the intervals where f is concave up and where f is concave down.

Verify that f(x) = x² + 3x -1 satisfies the hypothesis of the Mean-Value Theorem over the interval [0, 1] and find all values of C that satisfy the conclusion of the theorem.

An open cylindrical trash can is to hold 19 cubic feet of material. What should be its dimensions if the cost of material used is to be a minimum? [Surface Area, S = $\pi$ r² + 2 $\pi$ rh where r = radius and h = height.]

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 .

Answer true or false. A graphing utility can be used to show f(x) = |4x²| - 6 has two relative maxima on [-10, 10].

Find the point on the curve x² + y² = 64 closest to (7, 0).

The position function of a particle is given by s = t³ - 6t² - 8t for t $\ge$ 0. Find the functions for v and a.

Answer true or false. If f ''(-2) = -4 and f ''(2) = 4, then there must be an inflection point on (-2, 2).

Answer true or false. The triangle with the largest area that can be drawn inside a circle is an equilateral triangle.

Use a graphing utility to estimate the absolute minimum of f(x) = e ^x (ln x)⁶ on [1, 5].

Sketch a continuous curve having the following properties. f(-5) = 10, f(0) = 5, f(5) = 0, f'(x) > 0 for |x| > 5, f'(-5) = f'(5) = 0, f'(x) < 0 for x < 0, f'(x) > 0 for x > 0.

Find the relative extrema for f(x) = 3x + cos 2x, 0 < x < $\pi$ .

Answer true or false. A graphing utility can be used to show f(x) = |3x²| - 12 has two relative maxima on [-20, 20].

f(x) = |x - 8| has

Find the dimensions of the rectangular area of maximum area which can be laid out within a triangle of base 16 and altitude 4 if one side of the rectangle lies on the base of the triangle.

Answer true or false. The Mean-Value Theorem guarantees there is at least one c on [0, 1] such that f '(x) = 0.8 when f(x) = x.

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

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

Answer true or false. f(x) = e6x has a horizontal asymptote at y = 0.

If f(x) = x4 - 12x2 , find the intervals where f is concave up and where f is concave down.

Verify that f(x) = x2 + 3x -1 satisfies the hypothesis of the Mean-Value Theorem over the interval [0, 1] and find all values of C that satisfy the conclusion of the theorem.

An open cylindrical trash can is to hold 19 cubic feet of material. What should be its dimensions if the cost of material used is to be a minimum? [Surface Area, S = π\piπ r2 + 2 π\piπ rh where r = radius and h = height.]

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 .

Answer true or false. A graphing utility can be used to show f(x) = |4x2| - 6 has two relative maxima on [-10, 10].

Find the point on the curve x2 + y2 = 64 closest to (7, 0).

The position function of a particle is given by s = t3 - 6t2 - 8t for t ≥\ge≥ 0. Find the functions for v and a.

Answer true or false. If f ''(-2) = -4 and f ''(2) = 4, then there must be an inflection point on (-2, 2).

Answer true or false. The triangle with the largest area that can be drawn inside a circle is an equilateral triangle.

Use a graphing utility to estimate the absolute minimum of f(x) = e x (ln x)6 on [1, 5].

Sketch a continuous curve having the following properties. f(-5) = 10, f(0) = 5, f(5) = 0, f'(x) > 0 for |x| > 5, f'(-5) = f'(5) = 0, f'(x) < 0 for x < 0, f'(x) > 0 for x > 0.

Find the relative extrema for f(x) = 3x + cos 2x, 0 < x < π\piπ .

Sketch a continuous curve having the following properties. f(0) = 1, f(-1) = f(1) = 0; f '(x) > 0 for (- ∞\infty∞ ,0) and f '(x) < 0 for (0, + ∞\infty∞ ), f'(x) < 0 for (- ∞\infty∞ , + ∞\infty∞ ).

Answer true or false. A graphing utility can be used to show f(x) = |3x2| - 12 has two relative maxima on [-20, 20].

f(x) = |x - 8| has

Find the dimensions of the rectangular area of maximum area which can be laid out within a triangle of base 16 and altitude 4 if one side of the rectangle lies on the base of the triangle.

Answer true or false. The Mean-Value Theorem guarantees there is at least one c on [0, 1] such that f '(x) = 0.8 when f(x) = x.

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

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

Answer true or false. f(x) = e⁶^x has a horizontal asymptote at y = 0.

If f(x) = x⁴ - 12x²_,find the intervals where f is concave up and where f is concave down.

Verify that f(x) = x² + 3x -1 satisfies the hypothesis of the Mean-Value Theorem over the interval [0, 1] and find all values of C that satisfy the conclusion of the theorem.

An open cylindrical trash can is to hold 19 cubic feet of material. What should be its dimensions if the cost of material used is to be a minimum? [Surface Area, S = $\pi$ r² + 2 $\pi$ rh where r = radius and h = height.]

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 .

Answer true or false. A graphing utility can be used to show f(x) = |4x²| - 6 has two relative maxima on [-10, 10].

Find the point on the curve x² + y² = 64 closest to (7, 0).

The position function of a particle is given by s = t³ - 6t² - 8t for t $\ge$ 0. Find the functions for v and a.

Use a graphing utility to estimate the absolute minimum of f(x) = e ^x (ln x)⁶ on [1, 5].

Find the relative extrema for f(x) = 3x + cos 2x, 0 < x < $\pi$ .

Answer true or false. A graphing utility can be used to show f(x) = |3x²| - 12 has two relative maxima on [-20, 20].