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Quizzes

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!
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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.
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?

 PICTURE: mult choice 2-5 without red



x1

0
x2

x3

Q. The graph shows a function f

 PICTURE: mult choice 2-3 

 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. 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 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.
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