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m371-f10-hw2 - f x inside a b(b Let f x = log x-sin x Prove...

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Homework 2 Math 371, Fall 2010 Assigned: Thursday, September 16, 2010 Due: Thursday, September 23, 2010 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
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Unformatted text preview: 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 bisection method with starting interval [4 , 6]. (2) (Order of Convergence) Apply the theorems on pp. 90-91 to the following problems: (a) Section 2.3 #8 (b) Section 2.3 #9 1...
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