solve the second for y...
y=16-2x, then the A=xy becomes:
A=x(16-2x)
A=16x-2x^2
dA/dx=16-4x, d2A/dx2=-4
Since acceleration, d2A/dx2, is a constant negative, when velocity, dA/dx=0, A(x) is at an absolute maximum value...
dA/dx=0 when 4x=16, x=4 and that maximum value is:
A(4)=16x-2x^2=32 u^2