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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 real-valued 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 suﬃce 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 non-differentiable anywhere? Is there a local maximum or minimum at this point? (d) Does the function have any local maxima or minima at its end-points?...
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- Fall '08
- Optimization, non-negative real numbers, appropriate calculus conditions