[tex]f(x)=x^3+x^2+x[/tex]
[tex]\implies f'(x)=3x^2+2x+1[/tex]
[tex]\implies f''(x)=6x+2[/tex]
Inflection points occur where [tex]f''(x)=0[/tex] and provided that [tex]f(x)[/tex] is differentiable at those points. This happens at
[tex]6x+2=0\implies 6x=-2\implies x=-\dfrac13[/tex]
So the inflection point is [tex]\left(-\dfrac13,f\left(-\dfrac13\right)\right)=\left(-\dfrac13,-\dfrac7{27}\right)[/tex].
