Calc Min And Max

Front 1

optimization problems you find

Back 1

min and max

Front 2

absolute and local

Back 2

its local if its a min but there is something within the interval which is more of a min?

Front 3

extreme value theorem

Back 3

if f is continuous on a closed interval, then f contains an abs max and abs min at some place

Front 4

if its at an endpoint,

Back 4

can't be both local and absolute max/min

Front 5

more on extreme value theorem

Back 5

if not continuous, then need not have extremes

if open interval, then maybe not extreme

Front 6

fermat's theorem

Back 6

if f has a local max or min at c, and if f'(c) exists, then f'(c) = 0

but sometimes if f'(c) = 0 there actually isn't a max or min

Front 7

critical number

Back 7

if f'(c) = 0 or f'(c) does not exist

if max or min, then definitely is a critical value of f

Front 8

closed interval method

Back 8

to find ABSOLUTE min and max values of continuous function on closed interval:

1. find critical numbers
2. find the values of f at the endpoints of the interval
3. the largest of the values from step 1 and step 2

take the smallest and largest of both as min and max