Second Derivative Test

what is second derivative

Suppose is a function of

that is twice differentiable at a stationary point


1. If

, then

has a local minimum at


2. If

, then

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.


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