Find dimensions of rectange with area of 64 sq ft but a minimum perimeter

64/xy

y=64/x

P=2x+2y

P=2x+2(64/x)

P'=2 - 128/x^2

x=8, -8

y= 8, -8

P''= 256/x^3

P''= 256/(-8)^3 is < 0 when x = -8

P is a minimum at x= -8 and y= -8

Are my x and y values right?? And do I use the negative number when finding the minimum perimeter or what?? Did I get the right answers??

HOW DO I GET THE CONCEPT OF OPTIMIZATION??