Calculus Analysis Questions and Answers

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

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

10. Ans: 2 sin x cos x

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

13. A. B. 11. For graph E, what are the left-hand and right-hand derivatives at x = a?ANSWER: 0 and -∞ C. D. E. a a a a a (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 continuous at a, then it is differentiable at a. T F If a function f is differentiable at a, then it is continuous 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. FIf a function f is continuous at a, then it is differentiable at a. T If a function f is differentiable at a, then it is continuous at a. FIf a function f has a limit at a, then it is continuous at a.