Max/Min of Polynomial Functions

[ddrsakuramax]

Homework Statement

Does anyone know a possible equation or way to solve for the Max and Min of a Polynomial Function without Calculus or the Derivative test??

Homework Equations

The Attempt at a Solution

 

[Dick]

I do if it's a quadratic. Complete the square. You can do similar tricks with some other special polynomials. Otherwise it's using derivatives.

 

[ddrsakuramax]

What if you are given the zeroes and the multiplicity of the zeroes?

 

[Dick]

It will tell you that the maxs and mins that aren't at zero are between the zeros, but it won't tell you much more about them. If you have, for example, a double zero at a, (x-a)^2 is a factor of the polynomial and you can say x=a is a max or a min depending on the sign of the rest of the terms, that is true.

 

[ddrsakuramax]

ooo alright thanks a lot!