Chapter 4.4, Problem 66E

For positive A, B, the force between two atoms is a function of the distance, r, between them:

$f(r)=-\frac{A}{r^2}+\frac{B}{r^3}r>0.$

1. (a) What are the zeros and asymptotes of f?
2. (b) Find the coordinates of the critical points and inflection points of f.
3. (c) Graph f.
4. (d) Illustrating your answers with a sketch, describe the effect on the graph of f of:
   1. (i) Increasing B, holding A fixed
   2. (ii) Increasing A, holding B fixed