Calculus: Partial Derivatives?

A=xy, xy=64, y=64/x p=2x+2y p=2x+2(64/x) p=2x+128/x p=(2x^2+128)/x dp/dx=(4x^2-2x^2-128)/x^2 dp/dx=(2x^2-128)/x^2 dp/dx=0 only when 2x^2=128 x^2=64, x=8ft p=(2x^2+128)/x p(8)=32ft (check...p(7)=32.29ft, p(9)=32.22ft) And since p=2x+2y 32=16+2y, y=8ft as well meaning that the perimeter of any rectangle with a given area is minimized when the rectangle is a square.

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