hw2 - Homework 2 Math 471 Fall 2007 Assigned Friday Due...

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Homework 2 Math 471, Fall 2007 Assigned: Friday, September 14, 2007 Due: Friday, September 21, 2007 Include a cover page Clearly label all plots using title , xlabel , ylabel , legend Use the subplot command to compare multiple plots Include printouts of all Matlab code, labeled with your name, date, section, etc. (1) (Rootfinding and Optimization) (a) Suppose f ( x ) is differentiable on [ a, b ]. Discuss how you might use a rootfinding method to identify a local extremum of f ( x ) inside [ a, b ]. (b) Let f ( x ) = log x - sin x . Prove that f ( x ) has a unique maximum in the interval [4 , 6]. (Note that log means natural logarithm.) (c) Approximate this local maximum using six iterations of the enclosure methods (Bisection and False Position) with starting interval [4 , 6]. (d) Approximate this local maximum using six iterations of the two fixed-point methods (Secant and Newton). For Newton’s Method, use p 0 = 4. For the Secant Method, use p 0 = 6 and p 1 = 4. (e) What is your best estimate for p , the location of the maximum?
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