# Second Derivative Test

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

with

is a maximum or minimum.If

is a two-dimensional function that has a local extremum at a point and has continuous partial derivatives at this point, then and . The second partial derivatives test classifies the point as a local maximum or local minimum. Source: mathworld.wolfram.comCategory: Bank

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