4 ( x + 7) ( 2 - x) expand
4 ( -x^2 - 7x + 2x + 14)
4 ( -x^2 - 5x + 14)
-4x^2 - 20x + 56
The max value occurs at x = - (-20) / [ 2 (-4) ] = 20 / -8 = - 5/2 = -2.5
Plugging this into the original function we find the max as
4( -2.5 + 7) ( 2 - -2.5) =
4 ( 4.5) ( 4.5) =
81