Unformatted text preview: Now, since f 00 < 0 for all x 6 = 0, x = 0 is not an inﬂection point of f . 3. Consider the function f ( x ) = 2 x 3 + 3 x 212 x4. The critical points of f are x 1 = 1 and x 2 =2. Moreover, f (1) = 0 and f (2) = 0. If f 00 ( x ) = 6(2 x + 1), classify each of x 1 and x 2 as local maximizers or local minimizers. Solution Since each of x 1 = 1 and x 2 =2 are zeros of f , we need only compute the signs of f 00 ( x 1 ) and f 00 ( x 2 ). A routine calculation shows that f 00 (1) > 0 and f 00 (2) < 0. Therefore, x 1 = 1 is a local minimizer of f and x 2 =2 is a local maximizer of f ....
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 Spring '08
 Smith
 Computer Science, Calculus, Derivative, Continuous function, Convex function

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