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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? -> Picture
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?

 PICTURE: mult choice 2-5 without red -> x1

5. The graph shows a function f

 PICTURE: mult choice 2-3 

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

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

-> y = -2x - 1

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

 PICTURE: mult choice 2-6 -> 1

8. Consider the function f shown below: 

 PICTURE: mult choice 2-4 -> 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.