Find minimum of a generic polynomial

Hi,

I have to write a script that involves expanding a polynomyc series up to a given degree and then find its minimum(s). What would be an efficient and fast way of computing it? Not sure how I would do it with a generic-degree polynomy.

As an example:

Given a series like

I'd like to program the script that expands the series up to a given degree N and then find its minima, probably derivating the function and evaluating on the points, but maybe there's a faster built-in solution.

Thank!

Answer 1

[Matt J]

roots(polyder(p)) will find the roots of the derivative of p. You can then evaluate the polynomial at all the roots to see where the smallest value is attained.

Example:

p=poly([0 3 4]);

r=roots(polyder(p));

x=linspace(-1,5,1000);

plot(x,polyval(p,x),r,polyval(p,r),'rx')

[Image Analyst]

Very clever/cool, Matt!