Figure 3.1 is a generic illustration of an optimization situation. As the DV increases, one consequence gets better, while the other gets worse. The OF is the sum of the two features (or some other...

Figure 3.1 is a generic illustration of an optimization situation. As the DV increases, one consequence gets better, while the other gets worse. The OF is the sum of the two features (or some other composite such as the product). Consider the sum in this exercise. Often, people illustrate the optimum of the OF as occurring at the crossover (about DV = 4.5 in this illustration). However, this is wrong. For a generic case of OF = f(DV) + g(DV), use mathematical analysis to show that the optimum happens when the slope of f is the negative of the slope of g. What conditions would make DV∗ equal to the DV at the point of the crossover of the two curves?