MATH 180 Study Guide - Final Guide: Maxima And Minima
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Problem 1 solution: find the derivative of each function. Do not simplify your answers. (a) log5(6 + sin x) (b) xsin x (c) tan 1(e1 x) Solution: (a) use the chain rule. d dx log5(6 + sin x) = Cos x (b) first rewrite the function as the exponential of a logarithm and simplify using a loga- rithm rule. xsin x = eln x sin x. Now use the chain and product rules. d dx xsin x = d dx esin x ln x. = esin x ln x [(sin x)(ln x) + (sin x) (ln x)] + cos x ln x(cid:19) x x (c) use the chain rule. d dx tan 1(e1 x) = Problem 2 solution: find a point (x, y) on the graph of y = + 4 nearest the point p = (0, 13). Hint: find the minimum value of the square of the distance between (x, y) and p . x2.
