Question

Solve the following:
Find the point of inflection from f(x)= x^3+x^2+x

Answer 1

`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=-\frac13`

So the inflection point is
`\left(-\frac13,f\left(-\frac13\right)\right)=\left(-\frac13,-\frac7{27}\right)`.