What is the maximum number of turns in the graph of this function? f(x) = x^4-x^3+3x+1

Question

What is the maximum number of turns in the graph of this function?


`f(x) = x^4-x^3+3x+1`

Answer 1

The maximum number of turns is 3

Explanation:

The given function is

`f(x)=x^4-x^3+3x+1`

The degree of this polynomial is 4.

If the degree of a given polynomial is n, then the polynomial has at least n-1 turns.

Therefore the number of turns of this 4th degree polynomial is at least 3.