Question: The acceleration due to gravity, g, varies with height above the surface of the earth, in a certain way. If you go down below the surface of the earth, g varies in a different way. It can be shown that g is given by
where R is the radius of the earth, M is the mass of the earth, G is the gravitational constant, and r is the distance to the center of the earth.
(a) Sketch a graph of g against r.
(b) Is g a continuous function of r? Explain your answer.
(c) Is g a differentiable function of r? Explain your answer.