The volume of a cube is L*W*H.
So with L = 24-2x, W = 24-2x and H = x you get:
V(x)=(24-2x)*(24-2x)*x=((24-2x)^2)*x=(5…
The max volume is found when the derivative of V(x) equals zero.
V'(x)=576-192x+12x^2=0
Solving that we get two points: x=12 and x=4
We try both solutions in the Volume equation:
V(4)=1024
V(12)=0
So the correct answer is 1024 when x=4.