1. warmup

2. Be seated before the bell rings DESK homework Warm-up (in your notes) Agenda : go over hw Hw quiz Notes lesson 3.2

3. Notebook Table of content Page 1 Learning Target 1 13) Extreme Values 14) Role’s Thm MVT LT2: State and use Rolle’s and Mean Value Theorem HW: p.174; 1-4,9- 11,27,31-34,37- 43odd,51

4. 3.2 Role’s Theorem An extreme value must occur if certain things happen in the graph. If __________________then ________________. Review: IVT? Continuous. Y-value is in the middle There exist a c such that f(c) = y.

5. 3.2 Role’s Theorem An extreme value must occur if certain things happen in the graph. If __________________then ________________. If f is continuous from [a, b], f Is differentiable from (a, b) and f(a) = f(b) Then there is at least one “c” value s.t f’(c) = 0.

6. Does Role’s Theorem apply? 1)No, b/c not cont. & diff 2) No, b/c 3) yes, Cont. Diff.

7. Find the c-value 3) yes, Cont. Diff. Then there is at least one “c” value s.t f’(c) = 0. Role’s Theorem: Rolling down the Hill

8. Mean Value theorem: If f is continuous [a,b] and differential (a,b), Then a b Instantaneous ROC = average ROC Steps #1 - #2 - #3 - Ex:

10. Decide if MVT can be apply. If so find the c guarantee by the MVT.