5.10 Introduction to Optimization Problems

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Now that we understand how derivatives can determine the maximum and minimum values on a graph, we can also apply this knowledge to word problems. Optimization problems can look a little bit scary at first, but the most important thing to remember is that you need to take the derivative of the function you are trying to optimize! (the function you’re trying to find a maximum or minimum value for)

Optimization is different from the problems that we’ve seen before because it usually adds one more variable that we have to account for. This, however, doesn’t mean that we will have a function with three variables; instead, you need to find a relationship between two of the variables so that you can get rid of one.