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hw5s - MAT 1330 Fall 2011 Assignment 5 Due WED Nov 16...

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MAT 1330, Fall 2011 Assignment 5 Due WED Nov 16, 8:30am at the beginning of class. Late assignments will not be accepted; nor will unstapled assignments. Instructor (circle one): Jason Levy Robert Smith? Olga Vassilieva Catalin Rada DGD (circle one): 1 2 3 4 Student Name Student Number By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature Question 1. Consider the function f ( x ) = x - 4 x 2 . Follow these steps to graph the function. (a) The domain of f is x 6 = 0 (b) The x -intercept(s) of f are f ( x ) = 0 x - 4 = 0 x = 4 (c) The derivative of f is f 0 = f 0 ( x ) = x 2 (1) - ( x - 4)(2 x ) x 4 = x (8 - x ) x 4 = 8 - x x 3 (d) The critical point(s) of f are f 0 ( x ) = 0 8 - x = 0 x = 8 1
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(e) The second derivative of f is f 00 = f 00 ( x ) = x 3 ( - 1) - (8 - x )3 x 2 x 6 = 2( x - 12) x 4 (f) The point(s) of inflection are Since f 00 ( x ) < 0 for x < 12 and f 00 ( x ) > 0 for x > 12 12 is the only inflection point (g) Find lim x 0 + f ( x ) = -∞ , lim x 0 - f ( x ) = -∞ (h) Find lim x →-∞ f ( x ) = 0 ,lim x →∞ f ( x ) = 0
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