Chapter 4.1

Definitions and Theorems:
Absolute Max/Min:  Only one of each.

-A function f has an absolute max (min) at c if f(c)  ( ) f(x) for all x in domain.

Extreme Value Theorem:  If f is a continuous function on a closed interval [a, b], then the function f has an absolute max valued f(c), and absolute min valued f (d) at some numbers             c, d, in [a, b]. 

Fermat’s Theorem: If f has a local max/min at c, and f ’(c) exists then f ‘(c) = 0. 

   Critical Numbers: a value of a function in the domain of f, such that f ‘(c) = 0 or f ‘(c) DNE.

Closed Interval Method: used to find absolute max/min, when F is continuous with a closed interval [a, b].

1. Find the values of f at the critical numbers of f in [a, b]

2. Find the values of f at the endpoints of the interval

The largest value is the absolute max., smallest value is the absolute min.