1. Absolute or Global Maximum Absolute or Global Minimum
4.1 Max & Min Values
Absolute or Global Maximum
Absolute or Global Minimum 1

2. Local or Relative Maximum Local or Relative Minimum
4.1 Max & Min Values
Local or Relative Maximum
Local or Relative Minimum 2

3. 4.1 Max & Min Values Extreme Value Thm:
If f is continuous on a closed interval [a, b], then f attains an absolute max & min at some #’s c & d in [a, b] 3

4. 4.1 Max & Min Values
A critical number of f is a number c in the domain of f such that either f (c) = 0 or f (c) does not exist. 4

5. 4.1 Max & Min Values See pg. 278 Ex 1- 4 & Fig 6 & 7 See pg. 2805

6. Ex 1: Find all local extrema of f(x).6

7. To find ABS Max’s & Min’s on a closed interval:
Find all values of f at each critical #.
Find the value of f at each endpoint.
Smallest = ABS Min
Largest = ABS Max 7

8. Ex 2: Find the absolute max & min values of f(x) on the interval 2  x  2.5.8

9. HW – 4.1 pg , 5, 9, 11, 15, 17, 22, 23, 25, 27 – 31 all, 41, 47, 49, 53, 55, 57, 67