The gravitational force exerted by the planet Earth on a unit mass at a distance r from the centre of the planet is F(r)={GMrR3GMr2for 0 where M is the mass of Earth, R is its radius, and G is the gravitational constant. In a previous assignment, you showed that F(r) is a continuous function. We now study differentiability of F(r).

(a) Calculate limh→0−F(R+h)−F(R)h.

(b) Calculate limh→0+F(R+h)−F(R)h.

(c) Use (a) and (b) to prove that F(r) is not differentiable at r=R.