15.4. Suppose that you are a manufacturer of widgets. At your current level of production, you have determined that each one unit increase in the production level will decrease the revenue by $0.28. Each unit of increase in the production level leads to a drop in costs of $0.34. Each day, your plant is improving efficiency, so each day the production level is expected to increase by 32 units. At what rate is the profit changing? Would you continue to increase the production? Why?
15.5. Prove that the exponential function of the form y = AeBx is an always increasing function of x (assuming that B is positive and A is positive). In other words, show that this function never reaches a maximum and then starts to decrease. Such functions are referred to as monotonically increasing.
15.6. Prove that the logarithmic function y = A + B ln(x) is a monotonically increasing function.