Question

The volume of a cube with sides of length `s` is given by `V =s^3`. What is the rate of change of the volume with respect to `s` when `s` is 6 centimeters?

Answer 1

`color(blue)(108cm^3)`

Explanation:

We are given the volume function:

`V=s^3`

The rate of change is found using the first derivative of this function. This is often called the gradient function, because it gives the gradient of a tangent line drawn at the specified point.

`(dV)/(ds)(s^3)=3s^2`

We now plug in `s=6`

`3s^2=3(6)^2=108(cm^3)/s`