Fall2011-HW2 - f x has a unique maximum in the interval[4...

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Homework 2 Math 371, Fall 2011 Assigned: Thursday, September 15, 2011 Due: Thursday, September 22, 2011 (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
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Unformatted text preview: 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) (a) Section 2.3 #8 (b) Section 2.3 #9 1...
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