Find the max and min values of f(x,y)=x^2 + y^2 + 4 over the region R={(x,y) : x^2 + 2(y^2) =< 3

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- November 15th 2012, 08:42 PMjessicadowningFind max/min values.
Find the max and min values of f(x,y)=x^2 + y^2 + 4 over the region R={(x,y) : x^2 + 2(y^2) =< 3

- November 15th 2012, 08:58 PMMarkFLRe: Find max/min values.
You want to equate the first partials to zero and solve the resulting system to find the critical points:

Solve the resulting system to find any critical points in the given region.

Now you want to use the second partials test for relative extrema:

Let be a critical point of and suppose and are continuous in a rectangular region containing .

Let .

i) If and , then is a relative minimum.

ii) If and , then is a relative maximum.

iii) If , then is not an extremum.

iv) If , then no conclusion can be drawn concerning a relative extremum.