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).
Contact the MathWorld Team
inflection point of
sin^3(t) near t=100
