Consider a function in 1-D. If has a relative extremum at , then either or is not Differentiable at . Either the first or second Derivative tests may be used to locate relative extrema of the first kind.

A Necessary condition for to have a Minimum (Maximum) at is

and

A Sufficient condition is and (). Let , , ..., , but . Then has a Relative Maximum at if is Odd and , and has a Relative Minimum at if is Odd and . There is a Saddle Point at if is Even.

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1999-05-25