Instantaneous rate of change

Question

The surface area, S, of a sphere of radius r feet is S = S(r) = 4 pi r^2. Find the instantaneous rate of change of the surface area with respect to the radius r at r = 2.

1) 32 pi

2) 16 pi

3) 64 pi

4) 4 pi

Answer 1

S(r) = 4 pi r^2

To get the rate of change, find the 1st derivative:

S'(r) = 8 pi r

If r = 2, S' = 16pi

Answer 2

The instantaneous rate of change of the surface area is the value of the derivative at that point:

At r = 2

The answer is #2