Chapter 2.6, Problem 13E

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

$g=\{\begin{array}{l}\frac{GMr}{R^3}\text{for}r<R\\ \frac{GM}{r^2}\text{for}r\ge R,\end{array}$

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.

1. (a) Sketch a graph of g against r.
2. (b) Is g a continuous function of r? Explain your answer.
3. (c) Is g a differentiable function of r? Explain your answer.