Question

what is the maximum number of turns in the graph of this functuion f(x) x^4-x^3+3x+1

Answer 1

As given by the question

There are given that the function

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

Now,

By the defination, a polynomial of n degree, has a maximum turning points of:

$n-1$

Therefore, if you have the polynomial given in the problem, which is a polynomial of degree 4, that means (n=4).

The maximum number of turns can be obtained as following:

$\begin{gathered} n-1=4-1 \\ =3 \end{gathered}$

Hence, the maximum number of turns in the graph is 3.