A Sufficient Condition for Judging the Extreme Values of Multivariate Functions Based on the First-order Partial Derivative
This paper gives the first order sufficient conditions for extreme values of binary functions by an analogy to the sufficient conditions for the extreme values of the unary function,and extends the conclusions to the n-variate functions where n is greater than or equal to 3.The sufficient condition is applicable to the judgement of stationary point and the point where the partial derivative doesn't exist.The proof of the conclusion only involves the Lagrange Mean Value Theorem and first order partial derivative.It is more direct and concise than the current sufficient condition of the extreme values of the multivariate functions.
multivariate functionsextreme valuessufficient conditionpartial derivativethe Lagrange Mean Value Theorem
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