Chapter 3 Test

Question 1

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

Answer 1

-13

Question 2

What is the average rate of change of the function y = 2x^ 2 + 3 between x = x1 and x = x2?

Answer 2

2(x2+x1)

Question 3

What is the slope of the secant line of the function y = 4x^ 2 − 2x + 1 between x = x1 and x = x2?

Answer 3

4x2 + 4x1 − 2

Question 4

What is the average rate of change of the function y = 4x^ 3 − 2 between x = x1 and x = x2?

Answer 4

4 (x2^2 + x2x1 + x1^2 )

Question 5

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

Answer 5

4x

Question 6

What is the slope of the tangent line of the function f (x) = 4x ^2 − 2x + 1 at x ?

Answer 6

8x − 2

Question 7

What is the slope of the tangent line of the function f (x) = −4x ^2 − 5x + 2 at x ?

Answer 7

−8x − 5

Question 8

Consider the function y = x ^2 − 3x + 2. What is the slope of the tangent line at x = 2?

Answer 8

1

Question 9

Consider the function y = x ^2 − 3x + 5.

At what value of x is the slope of the tangent line equal to 7?

Answer 9

5

Question 10

Consider the function y = x ^2 + x + 9.

At what value of y is the slope of the tangent line equal to 5?

Answer 10

15

Question 11

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 11

6

Question 12

The position of a car at time t is given by the function p (t) = t ^2 − t − 7. What is the velocity when p (t) = 5? Assume t ≥ 0.

Answer 12

7

Question 13

The position of a car at time t is given by the function p (t) = t ^2 − 3t − 26. At what time will the velocity of the car be 11? Assume t ≥ 0.

Answer 13

7

Question 14

The position of a car at time t is given by the function p (t) = t ^2 + 4t − 17. Where will the car be when it moves at a velocity of 10? Assume t ≥ 0.

Answer 14

4

Question 15

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

Answer 15

1

Question 16

Evaluate the derivative of the function: f (x) = (x − 2)^−1

Answer 16

−1/(x−2)^2

Question 17

Given that f(x)=√6x−3, evaluate f′(x)

Answer 17

3 / √6x−3

Question 18

Find the slope of the line tangent to f(x)=x^2−x at the point x=2.

Answer 18

3

Question 19

True or false?

The derivative of a function at a point x represents the instantaneous rate of change at x.

Answer 19

true

Question 20

A ball is rolling along the x-axis. Its position (in feet) at time x (in seconds) is given by f(x)=2√x. Find its instantaneous rate of change when x=9 seconds.

Answer 20

1/3 ft/sec