Thread: Inflexion point

How do I prove this?

Prove that curve
y=x^3+4x

Has one point of inflexion, but no tuning points.

A necessary condition for to be an inflection point is that

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 and notice that it does not change sign anywhere.