We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.


Derivatives: Going Off On a Tangent True or False

1. The graph below shows a function f and a line:


The line is

-> tangent to f at a

2. Each graph below shows a function f and a line. Which line is NOT tangent to its corresponding function?

-> B

3. Three of the following phrases mean the same thing. Which phrase does not mean the same as the others? -> slope of f at a
4. At which value of x is the slope of f closest to zero?

-> x1

5. The graph shows a function f

 Which derivative is greatest? -> f ' (x4)

6. Find the tangent line to f(x) = x2 at -1.

-> y = -2x – 1

7. What is f ' (2), where f is shown below: 

-> 1

8. Consider the function f shown below: 

Which statement is true? -> We can draw a tangent line to f at x2 but not at x1.

9. Use a local linearization to approximate cos(1.5), given that the derivative of cos(x) at π/2 is -1.

-> 3.07

10. Which of the following statements cannot be true of any function f? -> f is both continuous and differentiable.