MATH 140 Lecture Notes - Lecture 26: Mean Value Theorem, Inflection
5 Nov 2015
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The following material will be covered by the exam: max-min problems, methods for solving them: Use section 4. 1 (plugging in critical points) Second-derivative test: important theorems, max-min theorem, mean value theorem, antiderivatives, exponential growth and decay, graphing. Where the function is increasing and decreasing. = x3 3 + 6 x for 0 x 3. Find the maximum and minimum values of f . x (x o: using section 4. 1: (0) = 6: thus, the minimum value is (x. = 3 2 3 = 3 2 1 = 3 + 1. Suppose that g is continuous on [0, 3] and differentiable on (0, 3). Also assume that g has 5 zeroes on [0, 3]. What is the minimum number of critical numbers in the interval [0, 3]. Support your answer: there are at least 4 critical numbers on the interval [0, 3] by rolle"s theorem. and the maximum value is (3) f.
