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Second Derivative Test

Second Derivative Test

A method for determining whether a critical point is a relative minimum or maximum.

 

Three rules for the Second Derivative Test: positive f''=relative min, negative f''=relative max, zero/undefined=inconclusive.
Example using y=x³-3x+4: critical points (1,2) and (-1,6); y″=6x confirms (1,2) minimum, (-1,6) maximum.

 

 

See also

Second derivative, first derivative test, absolute minimum, absolute maximum