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 (Bronshtein
et al. 2004, p. 231). A sufficient condition is that 
be continuous at 
and that 
have opposite signs on the two
sides of 
in a neighborhood of 
(Strang and Herman 2016, §4.5).
