# Difference between revisions of "Math 22 Extrema of Functions of Two Variables"

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(Created page with " '''Return to Topics Page''' '''This page were made by Tri Phan'''") |
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+ | ==Relative Extrema of a Function of Two Variables== | ||

+ | Let <math>f</math> be a function defined on a region containing <math>(x_0,y_0)</math>. The function <math>f</math> has a relative maximum at <math>(x_0,y_0)</math> when there is a circular region centered at <math>(x_0,y_0)</math> such that | ||

+ | |||

+ | <math>f(x,y)\le f(x_0,y_0)</math> | ||

+ | |||

+ | for all <math>(x,y)</math> in <math>R</math>. | ||

− | + | The function <math>f</math> has a relative minimum at <math>(x_0,y_0)</math> when there is a circular region centered at <math>(x_0,y_0)</math> such that | |

− | + | ||

+ | <math>f(x,y)\ge f(x_0,y_0)</math> | ||

+ | |||

+ | for all <math>(x,y)</math> in <math>R</math>. | ||

## Revision as of 08:04, 18 August 2020

## Relative Extrema of a Function of Two Variables

Let be a function defined on a region containing . The function has a relative maximum at when there is a circular region centered at such that for all in .

The function has a relative minimum at when there is a circular region centered at such that for all in .

**This page were made by Tri Phan**