What are the absolute min and max of f(x,y)=xy^2 over a specific domain?

Thread starter der.physika
Start date Feb 27, 2010
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To find the absolute minimum and maximum of the function f(x,y)=xy^2 within the domain defined by x^2+y^2≤4, one must first identify critical points in the interior where x^2+y^2<4. After locating these critical points, it is essential to evaluate the function along the boundary defined by x^2+y^2=4. This approach ensures that both interior and boundary conditions are considered for determining the extrema. The analysis will lead to identifying the values of f(x,y) at these critical points and boundaries. Ultimately, this will yield the absolute minimum and maximum values of the function within the specified domain.

Feb 27, 2010

der.physika

Find the absolute min & absolute max of

f(x,y)=xy^2

with domain x^2+y^2\leq4

Please help

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Feb 27, 2010

Dick

Science Advisor

Homework Helper

Look for critical points on the interior x^2+y^2<4 and then check the boundary x^2+y^2=4. You should be able to at least get started.

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