MAXIMUM AND MINIMUM VALUES THE EXTREME VALUE THEOREM

MAXIMUM AND MINIMUM VALUES THE EXTREME VALUE THEOREM 1 2 f(x) is continuous on attains an absolute maximum f(c) and minimum f(d) value Closed interval [a, b] How to find absolute Max and Min 1. Find all critical points ( ƒ’= 0 , or ƒ’ undefined ) 2. Evaluate ƒ at all criticals and endpoints a, b 3. Take the largest value and the smallest EXAMPLE: Find: Absolute max and min EXAMPLE: Find: Absolute max and min (not closed interval) How to find absolute Max and Min

MAXIMUM AND MINIMUM VALUES How to find absolute Max and Min not closed interval [a, b) 1. Find all critical points ( ƒ’= 0 , or ƒ’ undefined ) 2. Evaluate ƒ at all criticals and endpoint a, 3. Take the largest value and the smallest (exclude it if at b) F 083

MAXIMUM AND MINIMUM VALUES How to find absolute Max and Min not closed interval (a, b) 1. Find all critical points ( ƒ’= 0 , or ƒ’ undefined ) 2. Evaluate ƒ at all criticals and 3. Take the largest value and the smallest (exclude it if at a or b) EXAMPLE: Find: Absolute max and min

MAXIMUM AND MINIMUM VALUES How to find absolute Max and Min not closed interval 1. Find all critical points ( ƒ’= 0 , or ƒ’ undefined ) 2. Evaluate ƒ at all criticals and 3. Take the largest value and the smallest (exclude it if at a or b) EXAMPLE: Find: Absolute max and min Remarks: Polynomial with odd degree no absolute max, no absoulte min Polynomial with even degree absolute max only or absoulte min only

MAXIMUM AND MINIMUM VALUES EXAMPLE: Find: Absolute max and min Remarks: Polynomial with odd degree no absolute max, no absoulte min Polynomial with even degree absolute max only or absoulte min only

MAXIMUM AND MINIMUM VALUES Term 101_Final Remarks: Sometimes graphing is an easer method