Think you’ve got your head wrapped around **Derivatives**? Put your knowledge to
the test. Good luck — the Stickman is counting on you!

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?

Picture

Picture

Picture

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*.

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?

PICTURE: mult choice 2-5 without red

0

Q. The graph shows a function *f*.

PICTURE: mult choice 2-3

Which derivative is greatest?

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. Find *f'*(*2*), where *f* and its tangent line at 2 are shown below:

PICTURE: mult choice 2-6

1

1/3

1/6

5/6

Q. Consider the function *f* shown below:

PICTURE: mult choice 2-4

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*?