I need a little help with finding absolute extrema bounded by a region.

Find the absolute extrema of over the region .

Therefore:

and

Where do I go from here and how?

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- Apr 13th 2009, 12:10 PMwilcofan3Absolute Extrema (two variables)
I need a little help with finding absolute extrema bounded by a region.

Find the absolute extrema of over the region .

Therefore:

and

Where do I go from here and how? - Apr 13th 2009, 12:15 PMJhevon
- Apr 13th 2009, 12:24 PMicemanfan
By the Extreme Value Theorem, the extremes of given the constraint are either at points where or on the border of the region (i.e. where , since this is an ellipse). Let . Using the method of Lagrange Multipliers,

Substituting back into

we have

Hence the minimum value of is

and the maximum value of is .