First we open the parenthesis.
\(4(-x^2 +5x + 84)\)
Then we open up parenthesis again.
\(-4x^2 + 20x + 336\)
When x = 0, the value is 336.
When x = 1, the value is 352.
When x = 2, the value is 360.
When x = 3, the value is also 360.
But we see when x = 2.5, the value is 361.
If x = 2.4, the value is 360.96
If x = 2.6, the value is 360.96.
So that means the medium value for x is 2.5, which makes the expression the maximum value.
For the maximum value of the expression, it is 361.
4(x + 7)(12 - x) expand to:
-4x^2 + 20x + 336 max will occur at x = - b/2a = -20 /(2(-4)) = 2.5
sub in that value in the equation to find the max is 361