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Verified Answer :

LammettHash

\(f(x)=x^3+x^2+x\)
\(\implies f'(x)=3x^2+2x+1\)
\(\implies f''(x)=6x+2\)

Inflection points occur where \(f''(x)=0\) and provided that \(f(x)\) is differentiable at those points. This happens at

\(6x+2=0\implies 6x=-2\implies x=-\dfrac13\)

So the inflection point is \(\left(-\dfrac13,f\left(-\dfrac13\right)\right)=\left(-\dfrac13,-\dfrac7{27}\right)\).

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