The volume of a cube is increasing at the rate of 8 cm³/s. How fast is the surface area increasing when the length of an edge is 12 cm?

Let x be the length of a side, V be the volume, and s be the surface area of the cube.

Then, V = x³ and S = 6x² where x is a function of time t.

It is given that y = f(x).

Then, by using the chain rule, we have:

Hence, if the length of the edge of the cube is 12 cm, then the surface area is increasing at the rate of ⇒f(x₁)<f(x₂) cm²/s.