MATH-UA 121 Lecture 3: Extremes
22 Sep 2016
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A point can be absolute but not local (endpoints) and local but not absolute. Evt (extreme value theorem)if is continuous on [a, b] then f achieves both an absolute maximum value and an absolute minimum value. Closed interval method: to find the absolute max and abs min on a closed interval for , find all critical points and endpoints. Then make a chart and plug these points into . Rolle"s theorem let be: continuous on [a,b] 2) differentiable on (a,b) 3) Mvt (mean value theorem) let be: continuous on [a,b] 2) differentiable on (a,b) To find intervals of inc/dec for , use if f is increasing . if f is decreasing. @ c. changes sign from to + around c, then there is a local min @ c. does not change signs around c, then is neither a local min nor a local max. Second derivative test: if is continuous around c and 1)
