Inflexion point

• June 5th 2009, 07:49 PM
Inflexion point
How do I prove this?

Prove that curve
y=x^3+4x

Has one point of inflexion, but no tuning points.
• June 5th 2009, 08:05 PM
Spec
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.