1. 3.1 Extreme Values
Absolute or Global Maximum
Absolute or Global Minimum

2. 3.1 Extreme Values
Local or Relative Maximum
Local or Relative Minimum

3. Ex 1: Identify all extrema.b c d e f g

4. Ex 1: Identify all extrema.b c d e f g

5. Ex 1: Identify all extrema.b c d e f g

6. Ex 1: Identify all extrema.b c d e f g

7. 3.1 Extreme 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.

8. Ex 2: Find the critical numbers of g.

9. Extreme Value Thm:
If f is continuous on a closed interval [a, b], then f attains an absolute max & absolute min at some x-values on [a, b]

10. To find Absolute Max’s & Min’s on a closed interval:
Find f  & all critical numbers.
Find the value of f at each critical number.
Find the value of f at each endpoint.
Smallest = Absolute Min
Largest = Absolute Max

11. Ex 3: Find the absolute max & min values of the function on the interval: ½  x  4

12. HW – 3.1 pg. 169 # 1, 2, 3 – 7 odds, # 9 – 12 all, # 13 – 41 EOO