- I'll hope to have the exams graded by Thursday.
-
Tue 3/23 Section 4.2 & 4.3 Read 4.4 and 4.5 -- we'll talk Thursday about how to put all this together to graph a function. Begin on-line homework for 4.3 (due Tue. 3/30)
- We saw how critical points are the starting points for finding extrema, as well as boundary points.
- They may not exist for a function (examples)
- Theorem 1: continuous on a closed interval implies max and min
- Example
- Theorem 3: extrema on a closed interval are at critical points or on boundaries
- Theorem 4: Rolle's Theorem. Rolle's theorem works backwards: we deduce the existence of a
critical point from an extremum:
- Examples:
- #1, p. 188
- #2
- #3
- #10 (do some algebra!)
- #61
- Mean Value Theorem:
Notice that Rolle's theorem is a special case (or corollary) of the Mean Value Theorem, yet the MVT is proven via Rolle's theorem!
- First Derivative Test:
- Examples:
- #45, p. 198
