(a) Greatest when x is increased
We can check by an example. Let x = 2, y = 3, z = 4. Then
Volume of box = 2 × 3 × 4 = 24 cu. units.
If we increase x by 1 unit, keeping the other same i.e,
x = 3, then new volume = 3 × 3 × 4 = 36 cu. units.
If we increase y by 1 unit keeping the others same, i.e.,
y = 4, then new volume = 2 × 4 × 4 = 32 cu. units
If we increase z by 1 unit keeping the other same, i.e.,
z = 5, then new volume = 2 × 3 × 5 = 30 cu. units.
Hence the increase in volume is greatest, when x increases.
You can check with other values also.
