Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, calculate the derivative when x = 4 mm. V'(4) = mm3/mm What does V'(4) mean in this situation?

Answer:V'(4) = 48 mm³/mmV'(4) means that the rate of change of volume with respect to side when the length of the side is 4 mmStep-by-step explanation:Data provided in the questionV is the volume of the cube with x as its sidesAlso, Volume of cube = side³thus,V = x³ mm³Now,Derivative of volume with respect to side x,[tex]\frac{\textup{dv}}{\textup{dx}}[/tex]  = [tex]\frac{d(\textup{x}^3)}{\textup{dx}}[/tex] or[tex]\frac{\textup{dv}}{\textup{dx}}[/tex]  = V'(x) = 3x²now,at x = 4 mmV'(4) = 3(4)²orV'(4) = 48 mm³/mmHere, V'(4) means that the rate of change of volume with respect to side when the length of the side is 4 mm