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Sagot :
As given by the question
There are given that the function
[tex]f(x)=x^4-x^3+3x+1[/tex]Now,
By the defination, a polynomial of n degree, has a maximum turning points of:
[tex]n-1[/tex]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:
[tex]\begin{gathered} n-1=4-1 \\ =3 \end{gathered}[/tex]Hence, the maximum number of turns in the graph is 3.
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