A=xy if 2x+y=16 find the maximum

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