Calculus 12

Calculus

Lesson 12 Extrema

Maxima or minima on an interval:

if is continuous on an then has both

a minimum and a maximum value (there may be more than one of each).

There can be many relative extrema in a given interval, but only one maximum

and only one minimum.

A Critical Number, c, occurs when (horizontal tangent) or

is undefined. ALL relative extrema occur at critical numbers or at the

endpoints of the interval or domain (although just because you have

undefined does not mean you have an extrema).

To find extrema on :

1) find all critical numbers

2) evaluate each

3) evaluate and

4) extrema are the highest and lowest values determined in (1) and (2)

Examples:

On to Lesson 13 - Rolle's and Mean Value Theorems