# Derivatives: Going Off On a Tangent Quiz

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?

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?

x1

0
x2

x3

Q. The graph shows a function f

Which derivative is greatest?

f ' (x1)
f ' (x2)
f ' (x3)
f ' (x4)
Q. Find the tangent line to f(x) = x2 at -1.

y = 2x + 1

y = -2x + 1

y = 2x – 1

y = -2x – 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 x1 but not at x2.

We can draw a tangent line to f at x2 but not at x1.

We can draw tangent lines to f at both x1 and x2.

We cannot draw tangent lines to f at either x1 or x2.

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.