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Unformatted text preview: CALCULUS FOR THE SOCIAL AND MANAGEMENT SCIENCES Math 52-10 Spring 2008 HOMEWORK IV- DUE March 25, at the beginning of class 1. The followingis the graph of the secondderivative y" of a function y = f(x): I ~II I (o)-)~ I 1- ;!. /" (Y.R. J-) I-~)- (- ~YOl. )- ') X--.- (a) Determine the location and type of each vertical asymptote of the graph of y. (b) The function y = f(x) has stationary points at x = -4, x = -1, x = 2, and x = 4; determine the type of each of these stationary points. (c) Determine whether the graph of y is concave up or down, or neither, at the points x=-3.5,x=-3,x= O,x = 0.5, and x = 5. Draw small diagrams to depict the type of each VA and Sp, and clearly denote which sign-chart you used in order to determine your answers 2. I havea functiony = f(x) for whosegraphthe linex+3y= 1actsas an obliqueasymptote (see diagram below); what does this allow you to say about the existence and location (if it exists) of a horizontalasymptotefor the graph of the derivative y' = f' (x)?f' (x)?...
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