MATH 180 Study Guide - Final Guide: Minimal Surface, Asymptote, Maxima And Minima
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Problem 1 solution: find the derivatives of the following functions: (a) ln(ln(x)) (b) x6 + sin(x) ex (c) tan(x2) + cot(x2) Solution: (a) we evaluate the derivative using the chain rule. d dx ln(ln(x)) = Problem 2 solution: let f (x) = 24x3 48x + 3. (a) find all local maxima and minima of f (x). (b) find the absolute maximum and minimum of f (x) on [0, 2]. Solution: (a) the function will attain local extreme values at its critical points, i. e. the values of x satisfying f (x) = 0. f (x) = 0. To classify these points, we evaluate f (x) on either side of each critical point to determine how f changes sign. f ( 1) = 24, f (0) = 48, f (1) = 24. Since f changes from positive to negative across x = q 2. 3 , the value of f ( q 2. 3 , the value of f (q 2.
