# Thread: Minimum and Maximum points of polynomials.

1. ## Minimum and Maximum points of polynomials.

When looking at polynomials other than quadratic and linear, assuming we are given a cubic function where it has a maximum in between 2 real roots such as 5 and 4. Can we say that it is a max/minimum at x= (5+4)/2 = 4.5???

Also at those points, the rate of change is 0 right?

2. ## Re: Minimum and Maximum points of polynomials.

Originally Posted by sakonpure6
When looking at polynomials other than quadratic and linear, assuming we are given a cubic function where it has a maximum in between 2 real roots such as 5 and 4. Can we say that it is a max/minimum at x= (5+4)/2 = 4.5???

Also at those points, the rate of change is 0 right?
No. but if it has only two real roots, that means one of its extrema is tangent to the x-axis. That means, one simple root and one double root, or a root of multiplicity 2

3. ## Re: Minimum and Maximum points of polynomials.

Originally Posted by sakonpure6
When looking at polynomials other than quadratic and linear, assuming we are given a cubic function where it has a maximum in between 2 real roots such as 5 and 4. Can we say that it is a max/minimum at x= (5+4)/2 = 4.5???

Also at those points, the rate of change is 0 right?
No. Sometimes the point right in between two roots can even be undefined. But you are right that at a minima and maxima, the rate of change is 0.

4. ## Re: Minimum and Maximum points of polynomials.

Originally Posted by Paze
No. Sometimes the point right in between two roots can even be undefined. But you are right that at a minima and maxima, the rate of change is 0.
Perhaps you mean by "undefined" it is not readily known. You could find it: if x0 = (x1+x2)/2, then f(x0) is known.