- I'll start by taking questions on any of the material for the exam: Sections 3.4-3.7, 3.9
- Apologies:
- Section 4.1 assignment has implicit differentiation questions, which we did not cover (section 3.8).
- A word on implicit differentiation (just using the chain rule, really).
- Return of section 3.9, p. 169, #40-45
- Some great pictures, but all are too small.
- Don't crowd yourself!
- Use a little extra paper....
-
Thu 3/18 Section 4.2 No new assignment in preparation for the exam
- 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:
