volume of sphere = 4/3 pi r^3
s(x) = 4/3 pi r^3 4/3 pi is a constant.
s'(x) = 4 pi r^2 The derivative is the rate of change
s''(x) = 8 pi r we are interested in the value r = 2
s(2) = 4/3 pi 8 = 32/3 pi
s'(2) = 4 pi 4 = 16 pi
s''(2) = 8 pi 2 = 16 pi
the positive number in the second derivative tells us that at r = 2 there is a min.