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Math1210 Weekly Assignment 8 Spring, 2016 (Graphing functions - Mean Value Thm 3.5, 3.6) instructor: Uid number: name: Instructions: Please show all of your work as partial credit will be given where appropriate, and there may be no credit given for problems where there is no work shown. All answers should be completely simplified, unless otherwise stated. No calculators or electronics of any kind are allowed. (Total of 35 points possible.) 1. (20 points) Sketch a graph of the following functions using calculus. Justify all your work (you may want to refer to the method on page 181 of the textbook). (a) f (x) = 3x4 − 20x3 12 (b) f (x) = x2 − 4x + 3 x2 − x − 2 Page 2 (c) f (x) = 2 cos2 (3x) for 0 ≤ x ≤ 2π Page 3 2. (10 points) Let f (x) be a continuous function and let f 0 (x) have the graph shown below. Sketch a graph for f (x) according to the information provided by its derivative; in particular, try and answer the following (a) Where is f (x) increasing/decreasing? (b) Where is f (x) concave up/down? (c) Where does f (x) attain local max/min? Page 4 Page 5 3. (5 points) John travelled 112 miles in 2 hours to go and visit his mom. She is worried about John speeding up too much, and when he arrives she asks him if he ever broke the speed limit of 55 mph. John says no, but is he telling the truth? [Hint: use Mean Value Theorem]. Page 6