What is the maximum value of $4(x + 7)(2 - x)$, over all real numbers $x$?

4 ( 7 + x) ( 2 - x)   =

4 ( 14 -5x - x^2)  =

-4x^2  -20x   +  56

This is a parabola  that opens downward...it will have a max.....

The x value that produces the  max  =    - (-20) / ( 2 *  -4)  =  20 / -8 =  - 5/2

And  the max is

-4 (-5/2)^2  - 20 (-5/2) + 56  =

-4 ( 25/4) +  50 +  56

-25 + 106  =

81