An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local maxima or local minima. For example, for the curve plotted above, the point is an inflection point.

The first derivative test can sometimes distinguish inflection points from extrema for differentiable functions .

The second derivative test is also useful. A necessary condition for to be an inflection point is . A sufficient condition requires and to have opposite signs in the neighborhood of (Bronshtein and Semendyayev 2004, p. 231).