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Unformatted text preview: ECO 310, Fall 2007 Problem Set 1: Review of Optimization Due in class on October 2 Question 1 Note: Your graph in part (a) should suggest how to proceed in parts (b)(e), but you must check the appropriate calculus conditions for your answers to those parts. Consider the realvalued function f defined over the interval [ 10 , 10] by f ( x ) = ( x ( x 4) if 10 x , 10 x (8 x ) if 0 < x 10 . (a) Sketch a rough graph of the function. Use a calculator or a computer program such as Mathematica if you can; else calculate a few values by hand. Integer values of x will suce to give you a good idea. (b) Find all critical points of the function. Identify the local maxima and minima. (c) Is the function discontinuous anywhere? Is the function nondifferentiable anywhere? Is there a local maximum or minimum at this point? (d) Does the function have any local maxima or minima at its endpoints?...
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 Fall '08
 StephenE.Morris

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