Question 1

The largest open interval over which f is concave up for f(x) = 6x3 + 4x2- 3x + 2 is

Accepted Answer

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

Question 2

A projectile is dropped, and reaches the ground at 140 m/s. How long does it take the projectile to reach ground? (Assume the position function is   , where a = -10   .)

Accepted Answer

A)  7 s 
B)  28 s 
C)  4.47 s 
D)  14 s 
E)  3.16 s 
A)  7 s 
B)  28 s 
C)  4.47 s 
D)  14 s 
E)  3.16 s

Question 3

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

Accepted Answer

Concave up

Question 4

Given   . Find all vertical, horizontal and oblique asymptotes.

Accepted Answer

@#IMG-DLM& so there is a verti

Question 5

Let s(t) = t5- 2t + 9 be a position function. The acceleration function a(t) =

Accepted Answer

A)  5t4 - 2 
B)  20t3 
C)  5t4 -2t 
D)  20t3 -2 
E)  20t4 
A)  5t4 - 2 
B)  20t3 
C)  5t4 -2t 
D)  20t3 -2 
E)  20t4

Question 6

Let s(t) = sin 4t be a position function of a particle. At   the particle's velocity is

Accepted Answer

A)  Positive 
B)  Negative 
C)  Zero 
A)  Positive 
B)  Negative 
C)  Zero

Question 7

An automobile starts from rest and travels 3 miles along a straight road in 6 minutes. Use the Mean-Value Theorem to show that at some instant during the trip its velocity was exactly 30 miles per hour.

Accepted Answer

Let s = f(t) be the position versus time

Question 8

Find values for x and y such that their product is a minimum if y = 7x -8.

Accepted Answer

Let x = one number and y = oth

Question 9

If f(x) = x(x + 3)3 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 10

Use a graphing utility to locate the value of x where f(x) = x4 - x + 6 has an absolute minimum, if it exists.

Accepted Answer

A)  1 
B)    
C)  0 
D)  None exists 
E)  -6 
A)  1 
B)    
C)  0 
D)  None exists 
E)  -6

Question 11

Find the relative extrema for f(x) = x2/3(6 - x).

Accepted Answer

Relative minimum at

Question 12

If   on [0, 1], find the value c that satisfies the Mean-Value Theorem. (Round to three decimal places.)

Accepted Answer

A)  0.333 
B)  0.192 
C)  0.181 
D)  0.481 
A)  0.333 
B)  0.192 
C)  0.181 
D)  0.481

Question 13

Find the maximum sum of 2 numbers given that the first plus the square of the second is equal to 28?

Accepted Answer

Let x = one number, y = the other number

Question 14

Answer true or false. For the position function graphed, the acceleration at t = 1 is positive.

Accepted Answer

A) True 
 B)False

Question 15

Does   satisfy the hypothesis of the Mean-Value Theorem over the interval [-1, 1]? If so, find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

No, since f is not d

Question 16

Let s = 3t2- 7t -5 be the position function of a particle. Find the maximum speed of the particle during the time interval 1$\le$ t $\le$ 4.

Accepted Answer

The maximu

Question 17

f(x) = cos(3x) has an absolute minimum on [0,  $\pi$] at x =

Accepted Answer

A)   $\pi$ 
B)    
C)  3 
D)  2 $\pi$ 
E)  None exist 
A)   $\pi$ 
B)    
C)  3 
D)  2 $\pi$ 
E)  None exist

Question 18

Find the relative extreme values for f(x) = |12 -4x| on the interval [-4, 4] and determine where those values occur.

Accepted Answer

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

Question 19

If f(x) = sin 8x (0,  $\pi$/4), find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 20

If f(x) = x(x - 8)5 , find the inflection points.

Accepted Answer

The answer of If f(x) = x(x - 8)5 ,...

The largest open interval over which f is concave up for f(x) = 6x³ + 4x²- 3x + 2 is

A projectile is dropped, and reaches the ground at 140 m/s. How long does it take the projectile to reach ground? (Assume the position function is , where a = -10 .)

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

Given . Find all vertical, horizontal and oblique asymptotes.

Let s(t) = t⁵- 2t + 9 be a position function. The acceleration function a(t) =

Let s(t) = sin 4t be a position function of a particle. At the particle's velocity is

An automobile starts from rest and travels 3 miles along a straight road in 6 minutes. Use the Mean-Value Theorem to show that at some instant during the trip its velocity was exactly 30 miles per hour.

Find values for x and y such that their product is a minimum if y = 7x -8.

If f(x) = x(x + 3)³ , find the intervals where f is concave up and where f is concave down.

Use a graphing utility to locate the value of x where f(x) = x⁴ - x + 6 has an absolute minimum, if it exists.

Find the relative extrema for f(x) = x^2/3(6 - x).

If on [0, 1], find the value c that satisfies the Mean-Value Theorem. (Round to three decimal places.)

Find the maximum sum of 2 numbers given that the first plus the square of the second is equal to 28?

Answer true or false. For the position function graphed, the acceleration at t = 1 is positive.

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [-1, 1]? If so, find all values of C that satisfy the conclusion of the theorem.

Let s = 3t²- 7t -5 be the position function of a particle. Find the maximum speed of the particle during the time interval 1 $\le$ t $\le$ 4.

f(x) = cos(3x) has an absolute minimum on [0, $\pi$ ] at x =

Find the relative extreme values for f(x) = |12 -4x| on the interval [-4, 4] and determine where those values occur.

If f(x) = sin 8x (0, $\pi$ /4), find the intervals where f is concave up and where f is concave down.

If f(x) = x(x - 8)⁵ , find the inflection points.

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

The largest open interval over which f is concave up for f(x) = 6x3 + 4x2- 3x + 2 is

A projectile is dropped, and reaches the ground at 140 m/s. How long does it take the projectile to reach ground? (Assume the position function is , where a = -10 .)

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

Given . Find all vertical, horizontal and oblique asymptotes.

Let s(t) = t5- 2t + 9 be a position function. The acceleration function a(t) =

Let s(t) = sin 4t be a position function of a particle. At the particle's velocity is

An automobile starts from rest and travels 3 miles along a straight road in 6 minutes. Use the Mean-Value Theorem to show that at some instant during the trip its velocity was exactly 30 miles per hour.

Find values for x and y such that their product is a minimum if y = 7x -8.

If f(x) = x(x + 3)3 , find the intervals where f is concave up and where f is concave down.

Use a graphing utility to locate the value of x where f(x) = x4 - x + 6 has an absolute minimum, if it exists.

Find the relative extrema for f(x) = x2/3(6 - x).

If on [0, 1], find the value c that satisfies the Mean-Value Theorem. (Round to three decimal places.)

Find the maximum sum of 2 numbers given that the first plus the square of the second is equal to 28?

Answer true or false. For the position function graphed, the acceleration at t = 1 is positive.

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [-1, 1]? If so, find all values of C that satisfy the conclusion of the theorem.

Let s = 3t2- 7t -5 be the position function of a particle. Find the maximum speed of the particle during the time interval 1 ≤\le≤ t ≤\le≤ 4.

f(x) = cos(3x) has an absolute minimum on [0, π\piπ ] at x =

Find the relative extreme values for f(x) = |12 -4x| on the interval [-4, 4] and determine where those values occur.

If f(x) = sin 8x (0, π\piπ /4), find the intervals where f is concave up and where f is concave down.

If f(x) = x(x - 8)5 , find the inflection points.

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

The largest open interval over which f is concave up for f(x) = 6x³ + 4x²- 3x + 2 is

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

Let s(t) = t⁵- 2t + 9 be a position function. The acceleration function a(t) =

If f(x) = x(x + 3)³ , find the intervals where f is concave up and where f is concave down.

Use a graphing utility to locate the value of x where f(x) = x⁴ - x + 6 has an absolute minimum, if it exists.

Find the relative extrema for f(x) = x^2/3(6 - x).

Let s = 3t²- 7t -5 be the position function of a particle. Find the maximum speed of the particle during the time interval 1 $\le$ t $\le$ 4.

f(x) = cos(3x) has an absolute minimum on [0, $\pi$ ] at x =

If f(x) = sin 8x (0, $\pi$ /4), find the intervals where f is concave up and where f is concave down.

If f(x) = x(x - 8)⁵ , find the inflection points.