Final answer:
To find the value of x for which the volume of the cuboid is a maximum, express the volume of the cuboid in terms of x, differentiate the volume formula with respect to x and set it equal to zero to find the critical points. Identify the value of x that gives the maximum volume and substitute this value back into the volume formula.
Step-by-step explanation:
To find the value of x for which the volume of the cuboid is a maximum, we need to express the volume of the cuboid in terms of x. Let's assume the length, width, and height of the cuboid are represented by L, W, and H, respectively. The volume of a cuboid is given by V = LWH. We can express L, W, and H in terms of x and then substitute them into the volume formula. Differentiate the volume formula with respect to x and set it equal to zero to find the critical points. From the critical points, identify the value of x that gives the maximum volume. Finally, substitute this value of x back into the volume formula to find the maximum volume.