Question 1

Sketch the graph of y = x3 - 9x2 + 24x - 3. Find any minima, maxima, and inflection points.

Accepted Answer

ly' = 3x² - 18x + 2

Question 2

Answer true or false. The Mean-Value Theorem can be used on f(x) = |x - 3| on [-5, 5].

Accepted Answer

A) True 
 B)False

Question 3

Sketch the graph of y = x3 + 12x2. Find any stationary points and any points of inflection.

Accepted Answer

y' = 3x² + 24x y'' = 6x + 24 Re

Question 4

Sketch the graph of y = x3-48x + 4. Find any stationary points and any points of inflection.

Accepted Answer

y' = 3x² - 48 y'' =

Question 5

On the interval (0, 2 $\pi$), f(x) = | sin x cos(2x)| has

Accepted Answer

A)  a relative maximum only 
B)  a relative minimum only 
C)  both a relative maximum and a relative minimum 
D)  no relative extrema 
E)  cannot be determined 
A)  a relative maximum only 
B)  a relative minimum only 
C)  both a relative maximum and a relative minimum 
D)  no relative extrema 
E)  cannot be determined

Question 6

A rectangle is to have an area of 32 in2. What should be its dimensions if the distance from one corner to the mid-point of a nonadjacent side is to be a minimum?

Accepted Answer

Let x, y, and D be as shown in

Question 7

Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

Accepted Answer

A = xy and x² + y²

Question 8

Two numbers sum to 42. Find the two numbers whose product is maximum.

Accepted Answer

A)  21, 40 
B)  7, 35 
C)  6, 39 
D)  21, 21 
E)  14, 28 
A)  21, 40 
B)  7, 35 
C)  6, 39 
D)  21, 21 
E)  14, 28

Question 9

Use Rolle's Theorem to show that f(x) = 4x3 + 5x - 1 does not have more than one real root.

Accepted Answer

Suppose f has more than one real root. L

Question 10

Sketch the graph of y = x4 -14x2 + 50. Find any extrema and any points of inflection.

Accepted Answer

y' = 4x³ - 28x y''

Question 11

If   on [0, 8], find the value c that satisfies the Mean-Value Theorem. (Round to three decimal places.)

Accepted Answer

A)  1.333 
B)  1.540 
C)  0.759 
D)  1.923 
E)  0.385 
A)  1.333 
B)  1.540 
C)  0.759 
D)  1.923 
E)  0.385

Question 12

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for   on [0, 4 $\pi$].

Accepted Answer

A) True 
 B)False

Question 13

Sketch the graph of y = x2(9 -x2). Find any extrema and any points of inflection.

Accepted Answer

y = 9x²- x⁴

Question 14

The equation, x3 - 4x - 17 = 0 has one real solution for 1 < x < 17. Approximate it by Newton's Method.

Accepted Answer

f(x) = x³ - x - 17 f(x) = 3x<

Question 15

A rectangular garden is to be laid out with one side adjoining a neighbor's lot and is to contain 507ft2. If the neighbor agrees to pay for half the dividing fence, what should the dimensions of the garden be to insure a minimum cost of enclosure?

Accepted Answer

Let x and y be the dimensions shown in t

Question 16

Find all relative extrema of f(x) = |x2 - 4|.

Accepted Answer

Relative minima at (

Question 17

Let s(t) = t9 -t be a position function of a particle. At 1 the particle's acceleration is

Accepted Answer

A)  negative 
B)  positive 
C)  zero 
A)  negative 
B)  positive 
C)  zero

Question 18

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x4 + 8

Accepted Answer

@#IMG-DLM& = 1 f '(x) = 4x³ 4x³

Question 19

Use Rolle's Theorem to prove that the equation 6x5 - 28x3 + 6 = 0 has at least one solution in the interval (0, 1).

Accepted Answer

If f(x) = x⁶ - 7x

Question 20

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

Accepted Answer

A)  -2.0 
B)  0.0 
C)  2.0 
D)  4.0 
E)  -4.0 
A)  -2.0 
B)  0.0 
C)  2.0 
D)  4.0 
E)  -4.0

Sketch the graph of y = x³ - 9x² + 24x - 3. Find any minima, maxima, and inflection points.

Answer true or false. The Mean-Value Theorem can be used on f(x) = |x - 3| on [-5, 5].

Sketch the graph of y = x³ + 12x². Find any stationary points and any points of inflection.

Sketch the graph of y = x³-48x + 4. Find any stationary points and any points of inflection.

On the interval (0, 2 $\pi$ ), f(x) = | sin x cos(2x)| has

A rectangle is to have an area of 32 in². What should be its dimensions if the distance from one corner to the mid-point of a nonadjacent side is to be a minimum?

Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

Two numbers sum to 42. Find the two numbers whose product is maximum.

Use Rolle's Theorem to show that f(x) = 4x³ + 5x - 1 does not have more than one real root.

Sketch the graph of y = x⁴ -14x² + 50. Find any extrema and any points of inflection.

If on [0, 8], find the value c that satisfies the Mean-Value Theorem. (Round to three decimal places.)

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for $Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for on [0, 4 \pi ].$ on [0, 4 $\pi$ ].

Sketch the graph of y = x²(9 -x²). Find any extrema and any points of inflection.

The equation, x³ - 4x - 17 = 0 has one real solution for 1 < x < 17. Approximate it by Newton's Method.

A rectangular garden is to be laid out with one side adjoining a neighbor's lot and is to contain 507ft². If the neighbor agrees to pay for half the dividing fence, what should the dimensions of the garden be to insure a minimum cost of enclosure?

Find all relative extrema of f(x) = |x² - 4|.

Let s(t) = t⁹ -t be a position function of a particle. At 1 the particle's acceleration is

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x⁴ + 8

Use Rolle's Theorem to prove that the equation 6x⁵ - 28x³ + 6 = 0 has at least one solution in the interval (0, 1).

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

Sketch the graph of y = x3 - 9x2 + 24x - 3. Find any minima, maxima, and inflection points.

Answer true or false. The Mean-Value Theorem can be used on f(x) = |x - 3| on [-5, 5].

Sketch the graph of y = x3 + 12x2. Find any stationary points and any points of inflection.

Sketch the graph of y = x3-48x + 4. Find any stationary points and any points of inflection.

On the interval (0, 2 π\piπ ), f(x) = | sin x cos(2x)| has

A rectangle is to have an area of 32 in2. What should be its dimensions if the distance from one corner to the mid-point of a nonadjacent side is to be a minimum?

Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

Two numbers sum to 42. Find the two numbers whose product is maximum.

Use Rolle's Theorem to show that f(x) = 4x3 + 5x - 1 does not have more than one real root.

Sketch the graph of y = x4 -14x2 + 50. Find any extrema and any points of inflection.

If on [0, 8], find the value c that satisfies the Mean-Value Theorem. (Round to three decimal places.)

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for on [0, 4 π\piπ ].

Sketch the graph of y = x2(9 -x2). Find any extrema and any points of inflection.

The equation, x3 - 4x - 17 = 0 has one real solution for 1 < x < 17. Approximate it by Newton's Method.

A rectangular garden is to be laid out with one side adjoining a neighbor's lot and is to contain 507ft2. If the neighbor agrees to pay for half the dividing fence, what should the dimensions of the garden be to insure a minimum cost of enclosure?

Find all relative extrema of f(x) = |x2 - 4|.

Let s(t) = t9 -t be a position function of a particle. At 1 the particle's acceleration is

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x4 + 8

Use Rolle's Theorem to prove that the equation 6x5 - 28x3 + 6 = 0 has at least one solution in the interval (0, 1).

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

Sketch the graph of y = x³ - 9x² + 24x - 3. Find any minima, maxima, and inflection points.

Sketch the graph of y = x³ + 12x². Find any stationary points and any points of inflection.

Sketch the graph of y = x³-48x + 4. Find any stationary points and any points of inflection.

On the interval (0, 2 $\pi$ ), f(x) = | sin x cos(2x)| has

A rectangle is to have an area of 32 in². What should be its dimensions if the distance from one corner to the mid-point of a nonadjacent side is to be a minimum?

Use Rolle's Theorem to show that f(x) = 4x³ + 5x - 1 does not have more than one real root.

Sketch the graph of y = x⁴ -14x² + 50. Find any extrema and any points of inflection.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for $Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for on [0, 4 \pi ].$ on [0, 4 $\pi$ ].

Sketch the graph of y = x²(9 -x²). Find any extrema and any points of inflection.

The equation, x³ - 4x - 17 = 0 has one real solution for 1 < x < 17. Approximate it by Newton's Method.

A rectangular garden is to be laid out with one side adjoining a neighbor's lot and is to contain 507ft². If the neighbor agrees to pay for half the dividing fence, what should the dimensions of the garden be to insure a minimum cost of enclosure?

Find all relative extrema of f(x) = |x² - 4|.

Let s(t) = t⁹ -t be a position function of a particle. At 1 the particle's acceleration is

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x⁴ + 8

Use Rolle's Theorem to prove that the equation 6x⁵ - 28x³ + 6 = 0 has at least one solution in the interval (0, 1).

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