Answer:
V'(4) = 48 mm³/mm
V'(4) means that the rate of change of volume with respect to side when the length of the side is 4 mm
Step-by-step explanation:
Data provided in the question
V is the volume of the cube with x as its sides
Also,
Volume of cube = side³
thus,
V = x³ mm³
Now,
Derivative of volume with respect to side x,
=
or
= V'(x) = 3x²
now,
at x = 4 mm
V'(4) = 3(4)²
or
V'(4) = 48 mm³/mm
Here, V'(4) means that the rate of change of volume with respect to side when the length of the side is 4 mm