Inflection Point

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).

REFERENCES:

Bronshtein, I. N.; Semendyayev, K. A.; Musiol, G.; and Muehlig, H. Handbook of Mathematics, 4th ed. New York: Springer-Verlag, 2004.