hw2_solutions

# hw2_solutions - Homework 2 Solutions Math 471 Fall 2006...

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Homework 2 Solutions Math 471, Fall 2006 Assigned: Friday, September 15, 2006 Due: Friday, September 22, 2006 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. Here is an example of two MATLAB scripts which, together, allow you to pass a pass a function into your code. This allows you to reuse your code for other functions. Program 1 function p=myfun(x), p=1/x-cos(x); return Program 2 function p=bisection(myfun, a, b, nmax), for n = 1 : nmax, p(n) = (a+b)/2; if(feval(myfun,p(n))*feval(myfun,a) < 0 ), b=p(n); else a=p(n); end end 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 ]. Roots of the derivative give possible locations of local extrema. (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.)

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