1. Warm up

2. Quick 3.1 Review

3. Extrema: Maximum (highest point) and minimum (lowest point) of a function
2 Types:
Absolute or global
Relative or local

4. Absolute Extrema
Absolute/global maximum: f(x) has an absolute max at x = c if f(c) ≥ f(x) for every x in the domain we are working on.
Absolute/global minimum: f(x) has an absolute min at x = c if f(c) ≤ f(x) for every x in the domain we are working on.

5. Absolute Max and Mins

6. Extreme Value Theorem
If f is continuous on [a, b], then f has both a minimum and a maximum on the interval.
f(x) is continuous on the interval [-1, 2], so by EVT, f(x) will have a minimum and a maximum on this interval.

7. Relative Extrema
Relative/ local maximum: f(x) has a local max at x = c if there is an open interval containing c and f(c) is a maximum
Relative/local minimum: f(x) has a local min at x = c of there is an open interval containing c, and f(c) is a minimum.

8. Rolle’s Theorem and the Mean Value Theorem
Section 3.2
Rolle’s Theorem and the Mean Value Theorem

9. Rolle’s Theorem
Let f be continuous on [a, b] and differentiable on (a, b). If f(a) = f(b), then there exists some c in (a, b) such that f’(c) = 0.

11. Mean Value Theorem

13. Homework
P. 176 # 1 – 21 EOO, 33, 39 – 47 odd, 55, 57, 67 – 71 odd