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

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.com

Category: Bank

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