- I'll start by taking questions on the related rates problems. A lot of you seemed to have trouble with it.
- Hand in homework: Section 3.9, p. 169, #40-45
- No new assignment in preparation for the exam
Tue 3/16 Section 4.2
- Definitions:
- Absolute maximum
- Absolute minimum
- They may not exist for a function (examples)
- Theorem 1: continuous on a closed interval implies max and min
- Example
- Definitions:
- local extrema
- critical point
- Theorem 2: if f(c) local extremum, then c is critical
- Finding maxes and mins
- 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:
