The volume of a cube with sides of length ss is given by V =s^3V=s3. What is the rate of change of the volume with respect to ss when ss is 6 centimeters?

1 Answer
Jun 2, 2018

color(blue)(108cm^3)108cm3

Explanation:

We are given the volume function:

V=s^3V=s3

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^2dVds(s3)=3s2

We now plug in s=6s=6

3s^2=3(6)^2=108(cm^3)/s3s2=3(6)2=108cm3s