1. A closed box has a fixed surface area A and a square base with side x .
   (a) Find a formula for the volume V of the box, as a function of x .
   (b) Find the rate of change of V with respect to x.
2. The revenue from selling q items is given by the formula R(q) = 500q - q^2
   and the total cost is given by C(q) = 150 + 10q . Write down a function that gives the total
   profit earned. Find the rate of change of total profit with respect to q.
3. For positive constants A and B, the force between two atoms in a molecule is given by
   f(r) = A/r^2 + B/r^3 where r > 0 is the distance between the atoms.
   What is the expression for the instantenous rate of change of force between the atoms with respect to distance?