The perimeter in this case will be:
p=2x+y and we are told that p=84yd so
2x+y=84
y=84-2x
Now for the area:
A=xy, and using y found above in this gives you:
A=x(84-2x)
A=84x-2x^2 now taking the derivatives gives you the velocity and acceleration of the area function...
dA/dx=84-4x and d2A/dx2=-4
Since the acceleration is a constant -4, when velocity is equal to zero it is at the absolute maximum value for the area function...
dA/dx=0 only when 84=4x, x=21
So the maximum possible area will occur when x=21
A(21)=84(21)-2(21^2)
A(21)=882 yd^2
