Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a so

Question

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) = mm^3/mm What does V'(4) mean in this situation? V'(4) represents the rate at which the volume is increasing as x reaches 12 mm.V'(4) represents the volume as the side length reaches 4 mm. V'(4) represents the rate at which the volume is increasing with respect to the side length as x reaches 4 mm.V'(4) represents the rate at which the side length is increasing with respect to the volume as x reaches 4 mm.V'(4) represents the rate at which the volume is increasing with respect to the side length as V reaches 12 mm^3.

Explanation / Answer

V = x^3
dV/dx = V'(x) = 3x^2
V'(4) = 3(42) = 48 mm3/mm

V'(4) represents the rate at which the volume is increasing with respect to the side length as x reaches 4 mm.

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