Question

The graph of a polynomial functions generally has several extreme points and is a smooth continuous curve. If n is odd, then the ends point (i.e the right and left side) in opposite directions. If n is even, the ends point the in the same direction. Why?

Answer 1

Explanation:

Because, if even , for example x^2, then the square of a negative and a positive x will always be positive.

For odd x, eg x^3 if x is negative x^3 is negative and if x is positive x^3 is positive.