# Derivatives: Going Off On a Tangent Quiz

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Derivatives**Q. The graph below shows a function

*f*and a line:

The line is

a secant line between

*a*and*b*tangent to

*f*at*a*tangent to

*f*at*b*none of the above

Q. Each graph below shows a function

*f*and a line. Which line is NOT tangent to its corresponding function?

A

B

C

D

Q. Three of the following phrases mean the same thing. Which phrase does not mean the same as the others?

slope of the tangent line to

*f*at*a*.*f '*(

*a*)

limit of secant lines between

*a*and*a*+ h as*h*approaches 0.slope of

*f*at*a*Q. At which value of

*x*is the slope of*f*closest to zero?

*x*

_{1}

0

*x*

_{2}

*x*

_{3}

Q. The graph shows a function

*f*.Which derivative is greatest?

*f*' (

*x*

_{1})

*f*' (

*x*

_{2})

*f*' (

*x*

_{3})

*f*' (

*x*

_{4})

Q. Find the tangent line to

*f*(*x*) =*x*^{2}at -1.*y*= 2

*x*+ 1

*y*= -2

*x*+ 1

*y*= 2

*x*– 1

*y*= -2

*x*– 1

Q. What is

*f '*(2), where*f*is shown below:

0

1

1/6

5/6

Q. Consider the function

*f*shown below:Which statement is true?

We can draw a tangent line to

*f*at*x*_{1}but not at*x*_{2}.We can draw a tangent line to

*f*at*x*_{2}but not at*x*_{1}.We can draw tangent lines to

*f*at both*x*_{1}and*x*_{2}.We cannot draw tangent lines to

*f*at either*x*_{1}or*x*_{2}.Q. Use a local linearization to approximate cos(1.5), given that the derivative of cos(

*x*) at π/2 is*-*1.0.07

0.2

2.2

3.07

Q. Which of the following statements cannot be true of any function

*f*?*f*is both continuous and differentiable.

*f*is continuous but not differentiable.

*f*is not continuous but is differentiable.

*f*is neither continuous nor differentiable.