What is the maximum value of 4(x + 7)(2 - x) + 4(x + 7)(6 - x), over all real numbers x?
+130020 4 ( x + 7)(2-x) + 4(x + 7) (6-x) =
4[ 2x + 14 -x^2 - 7x ] + 4 [ 6x + 42 -x^2 -7x ] =
4 [ -x^2 -5x + 14 ] + 4 [ -x^2 -x + 42 ]
-4x^2 -20x + 56 - 4x^2 -4x + 168
-8x^2 - 24x + 224
This is a parabola with the x coordinate of the vertex given by -b/ (2a) = 24 / ( 2 *-8) = 24/ -16 =- 1.5
And y coordinate of the vertex is the max = -8(-1.5)^2 -24(-1.5) + 224 = -18 + 36 + 224 = 242
