Chapter 3 Practice Test

Question 1

What is the average rate of change of the function y = 2x ^2 + 3 between x = 2 and x = 4?

Answer 1

12

Question 2

What is the slope of the secant line of the function y = 4x ^2 − 2x + 1 between x = 3 and x = 6?

Answer 2

34

Question 3

What is the average rate of change of the function y = 4x^ 3 − 2 between x = 2 and x = 4?

Answer 3

112

Question 4

What is the slope of the secant line of the function y = −2x ^2 + 3x − 1 between x = x1 and x = x2?

Answer 4

−2x1 − 2x2 + 3

Question 5

The position of a car at time t is given by the function p (t) = t^ 2 − 4t − 18. Where will the car be when its velocity is 10? Assume t ≥ 0.

Answer 5

3

Question 6

Apply the definition of the derivative to differentiate the function f (x) = 6.

Answer 6

0

Question 7

Differentiate the function f (x) = 2x.

Answer 7

2

Question 8

Evaluate f′(x) if f(x)=√x+1.

Answer 8

1/2√x+1

Question 9

Find the derivative of the function: f (x) = 2x ^2.

Answer 9

4x

Question 10

Evaluate the following as true or false: The derivative of a function f (x) at a point x0 is equal to the equation of the line tangent to f (x) at the point x0.

Answer 10

false

Question 11

Find the slope of a line tangent to f (x) = x^3 at the point (x, f (x)).

Answer 11

3x^2

Question 12

Find the equation (in point-slope form) of the line tangent to f(x)=3x^2−2 at the point x=−3.

Answer 12

y−25=−18(x+3)

Question 13

The instantaneous rate of change of a ball (in ft/s) is given by f′(x)=1√x. When was the ball traveling 2 ft/s?

Answer 13

1/4 sec

Question 14

True or false?
The instantaneous velocity at time t is defined as the average velocity between the initial time and the exact instant t.

Answer 14

false

Question 15

Consider the function

y = x^ 2 − x + 7. What is the equation of the tangent line at x = 2?

Answer 15

y − 9 = 3 (x − 2)

Question 16

The position of a car at time t is given by the function p (t) = t ^2 − 2t − 4. What is the velocity at t = 2? Assume t ≥ 0.

Answer 16

2

Question 17

The position of a car at time t is given by the function p (t) = t ^2 + 2t − 4. What is the velocity when p (t) = 11? Assume t ≥ 0.

Answer 17

8

Question 18

The position of a car at time t is given by the function p (t) = t ^2 − 3t − 6. At what time will the velocity of the car be 7? Assume t ≥ 0.

Answer 18

5

Question 19

What is the derivative of the function f (x) = 4x ^3 − 2 at x = 4?

Answer 19

192

Question 20

What is the derivative of the function f = 2x^ 2 + 3 at x = 2?

Answer 20

8