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/xcos(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.)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '08
 LinZhi
 Math, Calculus, Numerical Analysis, Optimization, Logarithm, Secant method, Rootfinding algorithm

Click to edit the document details