Calculus Review - Applications of Derivatives

1.

Multiple Choice

3 mins

1 pt

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle?

v(t) = -2

v(t) -2t - 1

v(t) = t³

v(t) = -t

2.

Multiple Choice

3 mins

1 pt

Where does the function, f(x) = 2x³ - 9x²+ 12x -3 have relative max/min values?

Rel max x = -1, Rel min x = 2

Rel min x = 1, Rel min x = 2

Rel max x = 1, Rel min x = 2

Rel max x = 2, Rel min x = 1

3.

Multiple Choice

3 mins

1 pt

Let f be the function with derivative given by f'(x) = x² - 2/x. On which of the following intervals is f decreasing?

(-∞, 0]

(-1, 0]

(0, ∛2]

(∛2, ∞)

4.

Multiple Choice

2 mins

1 pt

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

increasing

decreasing

concave up

concave down

5.

Multiple Choice

2 mins

1 pt

Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.

an inflection point

a critical point

a minimum

a maximum

6.

Multiple Choice

2 mins

1 pt

The slope of a function is described by its ____________.

first derivative

second derivative

third derivative

expression

7.

Multiple Choice

3 mins

1 pt

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

0

-1

2

5

8.

Multiple Choice

2 mins

1 pt

If a function has a derivative that is negative, what does that tell you?

The function is increasing

The function is decreasing

The function is concave up

The function is concave down

9.

Multiple Choice

2 mins

1 pt

What is a point of inflection?

When a function goes from increasing to decreasing

When a function goes from concave up to concave down

10.

Multiple Choice

2 mins

1 pt

If a function has a second derivative that is negative, what does that tell you?

The function is increasing

The function is decreasing

The function is concave up

The function is concave down

11.

Multiple Choice

2 mins

1 pt

If a function has a second derivative that is positive, what does that tell you?

The function is increasing

The function is decreasing

The function is concave up

The function is concave down

12.

Multiple Choice

2 mins

1 pt

Over what interval(s) is f(x) decreasing?

(-3, 1)

(-∞, -5) ∪ (0, 2)

(-∞, -3) ∪ (1, ∞)

(-5, 0) ∪ (2, ∞)

13.

Multiple Choice

3 mins

1 pt

The derivative f'(x) of the function f(x) is shown. On what interval(s) is the FUNCTION f(x) increasing?

(-∞, -1) only

( 3, ∞) only

(-∞, -1) and ( 3, ∞)

(1, ∞)

14.

Multiple Choice

3 mins

1 pt

Find the x-coordinate of the inflection point of f(x)=6x²-x³.

-2

0

2

None

15.

Multiple Choice

5 mins

1 pt

A rectangular solid that has a square base has a surface area of 150 square inches. Find the maximum volume of the solid. (use Calculus)

5

125

150

250

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