# Math Help - Inflexion point

1. ## Inflexion point

How do I prove this?

Prove that curve
y=x^3+4x

Has one point of inflexion, but no tuning points.

2. A necessary condition for $x$ to be an inflection point is that $f''(x)=0$

Since there's only one solution to this equation for this function, there is at most one inflection point.

To prove that there's no turning point, study $f'(x)$ and notice that it does not change sign anywhere.