Answers:
V = (15-2x)(8-2x)x
V = 120x -46x²+ 4x³
V' = 120 -92x + 12x²
0 = 120 -92x + 12x²
x = (92±52)/24
x = 6 or 5/3
Pick x = 5/3
Volume = (15-2*5/3)(8-2*5/3)*5/3
= 90.74 inÂł
To justify x = 5/3 is the max
V" = -92 + 24x
V"(5/3) = -92 + 24(5/3) <0 negative.
Volume V(5/3) is max because the function is
concave down with V"<0.