How do I prove this?

Prove that curve

y=x^3+4x

Has one point of inflexion, but no tuning points.

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- Jun 5th 2009, 07:49 PMEmililypadInflexion point
How do I prove this?

Prove that curve

y=x^3+4x

Has one point of inflexion, but no tuning points. - Jun 5th 2009, 08:05 PMSpec
A necessary condition for $\displaystyle x$ to be an inflection point is that $\displaystyle f''(x)=0$

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 $\displaystyle f'(x)$ and notice that it does not change sign anywhere.