MATA32H3 Lecture Notes - Lecture 6: Maxima And Minima, Profit Maximization
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MATA32H3 Full Course Notes
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If f is continuous and differentiable on an open interval i, then if f (x) > 0 for all x i, if f (x) < 0 for all x i, Example 6. 1: find the intervals of increasing and intervals of decreasing of f(x) = for x r. Then we need to test" them to find out if they are relative extrema. Let f be differentiable on (a, b). c (a, b) is a critical value of f. Example 6. 2: find all relative extrema of y = x2. Example 6. 3: find all relative extrema of y = x2ex. Example 6. 4: find all relative extrema of f(x) = relative max or min. )3 for x r and determine if they are. Let c dom f. f(c) is an absolute maximum for f if f(c) is an absolute minimum for f if f(c) is an absolute extremum for f if.
