Math 22 Extrema of Functions of Two Variables

Relative Extrema of a Function of Two Variables

 Let $f$ be a function defined on a region containing $(x_{0},y_{0})$. The function $f$ has a relative maximum at $(x_{0},y_{0})$ when there is a circular region  centered at $(x_{0},y_{0})$ such that
 
 $f(x,y)\leq f(x_{0},y_{0})$
 
 for all $(x,y)$ in $R$.

 The function $f$ has a relative minimum at $(x_{0},y_{0})$ when there is a circular region  centered at $(x_{0},y_{0})$ such that
 
 $f(x,y)\geq f(x_{0},y_{0})$
 
 for all $(x,y)$ in $R$.

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