Second Derivative Test
Suppose is a function of
that is twice differentiable at a stationary point
has a local minimum at
has a local maximum at
The extremum test gives slightly more general conditions under which a function
is a maximum or minimum.
is a two-dimensional function that has a local extremum at a point
and has continuous partial derivatives at this point, then
. The second partial derivatives test classifies the point as a local maximum or local minimum.