1. Over what interval(s) is f increasing?
1. Consider f ‘ (x) shown
Over what interval(s) is f increasing?

2. Slopes are positive everywhere except x = 0
(-∞,0) U (0,∞)

3. Ans: 12 f ‘ (x)

4. Ans: sec 2 x

5. Ans: 2e 2x

6. Ans: -12x -13

7. Ans: 0

8. Ans: -csc x cot x

9. Ans: ax ln a

10. Ans: 2 sin x cos x

12. a A. B. C. D. E.
11. For graph E, what are the left-hand and right-hand derivatives at x = a?

13. a A. B. C. D. E.
11. For graph E, what are the left-hand and right-hand derivatives at x = a? ANSWER: 0 and -∞
(At vertical tangents, as with limits, if we write f’ (a) =  it means the slope “approaches ”, but that is not a real number slope.)

14. Ans: -csc2x

16. 14. Must get all three correct to count the point.
T F If a function f is differentiable at a, then it is continuous at a.
T F If a function f is continuous at a, then it is differentiable at a.
T F If a function f has a limit at a, then it is continuous at a.

17. 14. Must get all three correct to count the point.
T If a function f is differentiable at a, then it is continuous at a.
F If a function f is continuous at a, then it is differentiable at a.
F If a function f has a limit at a, then it is continuous at a.