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. If 
is twice differentiable at an inflection point
, then the necessary
condition 
holds. However, an inflection point may occur where the second derivative does not
exist. A sufficient condition is that 
have opposite signs on the two sides of 
in a neighborhood of 
(Bronshtein and Semendyayev 2004,
p. 231).
