Detrmine the maximum value and the min value of f(x,y)= x^2+y^2-x-y on the closed unit disc D: x^2+y^2<=1.

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- March 8th 2013, 09:35 AM #1

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- March 8th 2013, 10:14 AM #2

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## Re: max/min

If a max or min occurs in the interior of the disk, then they will occur where f_x= 2x- x= 0 and f_y= 2y- y= 0.

But it is also possible that the max and/or min occurs on the bounding circle. On that circle, x= cos(t), y= sin(t) so that f(x,y)= f(t)= 1- cos(t)- sin(t). The max or min will occur where f'(t)= sin(t)- cos(t)= 0