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.
(Rootfnding and Optimization)
(a) Suppose
f
(
x
) is di±erentiable on [
a, b
]. Discuss how you might use a root²nding method to identify
a local extremum of
f
(
x
) inside [
a, b
].
Roots of the derivative give possible locations of local extrema.
(b) Let