Week 9 Calculus I Outline of Notes

by S. Gramlich

(updated 12/11/06)

I) 4.1 Max & Min Values= hi/lo dvs but stated @ iv

absolute (global) max/min; local (relative) max/min; *endpts can't be local

Def (p. 279, 280) & Extreme Value Thm (p. 281)

Fig 1, p. 279

Fermat's Thm, p. 282 (& rephrased p. 283)

Critical # (c) Def, p. 283

Closed Interval Method: find abs max/min

1. find c from f'(c) = 0 & f(c)

2. given endpoints a & b, find f(a), f(b)

3. hi f =max, lo f=min

4.1, p. 287, #56

II) 4.2 for existence of c

Rolle's Thm:

if 1. f cont (see sec 2.5), 2. f diff (see 2.9, p. 170),

3. f(a) = f(b) then f'(c)=0

verify 1,2 algebraically & graphically, 3 algebraically then find c

4.2, p. 295, #4

Mean Value Thm:

if 1. f cont, 2. f diff then f'(c)= [f(b)-f(a)]/(b-a)

verify 1, 2 algebraically & graphically then find c

4.2, p. 295, #14