Find the instantaneous rate of change of the surface area s ! 6x2 of a cube with respect to the edge length x at x ! a

The instantaneous rate of change is simply equivalent to the first derivative of the equation or function. We are given the equation of Surface Area (A) with respect to side (x):

A = 6 x^2

Taking the first derivative of the equation:

dA = 12 x dx

dA / dx = 12 x

Now the term dA / dx is the instantaneous rate of change in the surface area with respect to the side length. To get the rate of change when the side x = a, simply plug this in into the equation:

rate of change = dA / dx = 12 x

so when x = a:

rate of change = 12 a

answer: a.   one is a factor of every whole number since every number is divisible by itself.