# Thread: Simple Point of Inflection and Critical Point Question

1. ## Simple Point of Inflection and Critical Point Question

Hey I was just wondering if your critical point and point of inflection can be the same?

Or if you work it out and the Point of inflection turns out the same then, the Point of inflection does not exist? or can the co exist at the same spot?

2. y=x^3 at x=0

3. Originally Posted by lostsheep
Hey I was just wondering if your critical point and point of inflection can be the same?

Or if you work it out and the Point of inflection turns out the same then, the Point of inflection does not exist? or can the co exist at the same spot?
an inflection point is a point where the concavity changes, this does not happen for other extrema (maximums and minimums), so an inflection point cannot coincide with said critical points

critical points are points where the first derivative is zero, there are cases when an inflection point fulfills this condition (see curvature's example)