Problem Set 3 230 Sec 870 - F2016 (1).pdf

Problem Set 3 230 Sec 870 - F2016 (1).pdf - MAT 230 870 P...

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MAT 230 870 PROBLEM SET 3 F2016 P. Mazur (29 Pts) (9) 1. Let 3 2 2 3 72 12 f x x x x . Use the methods of Calculus to determine the following. Each numerical answer should be written in exact form and you must use Calculus to justify each answer. Reading values off of a graph will not earn any credit.: a) What are the critical value(s) for f(x)? _________________ b) Name any point(s) which is/are a local maximum for f(x). _________________ c) Name any point(s) which is/are a local minimum for f(x). _________________ d) Name any point(s) which is/are points of inflection for f(x). _________________ e) On what interval(s) is f(x) increasing? _________________ f) On what interval(s) is f(x) decreasing? _________________ g) On what interval(s) is the graph of f(x) concave up? _________________ h) On what interval(s) is the graph of f(x) concave down? _________________
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(12) 2. Sketch the graph of 2 3 3 1 x x g x x . Using the methods of Calculus, determine the following facts about the graph of g(x) using the methods of Calculus. Your graph should reflect your answers to the questions.
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