\(f'(x)=0 \iff\) Extremum ... right?

Calculus Level 4

\[f(x)=(x^2-1)^{n+1}(x^2+x+1), ~n \in \mathbb{N}\] If this function has an extremum at \(x=1\), what is/are the possible value(s) of \(n\)?

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