Question

What is the maximum number of extrema that a function with degree 8 could have

Answer 1

Given:

A function with degree 8.

Any polynomial function of degree n has at most n−1 local extrema.

This is because to get extreme points of a function, we differentiate and when we differentiate a function of degree 8, the resulting function will be of degree 7.

Therefore, a function of degree 8 could have at most 7 number of extrema.