Unit 5 ends with a return to a realistic context. To optimize something means to find the best way to do it. “Best” or “optimum” may mean the quickest, the cheapest, the most profitable, or the easiest way to do something.

For example, you may be asked to build a box of a given volume with the least, and therefore cheapest, amount of material. Thus, these are really problems where you need to find the maximum or minimum of the function that models the situation.  There are applications to engineering, finance, science, medicen, and economics among others.

The most difficult part of these problems is often writing the equation to be optimized; not the calculus involved. Once you have the model, finding the extreme value is easy.

The last part of this unit extends the ideas of this unit to implicit relations, those whose graph may not be a function. These too, increase, decrease, and have extreme values. The same techniques help you to find them.  

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Course and Exam Description Unit 5 Sections 11 and 12

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A note for teachers: You are not behind scheduel. Please remember that I am posing this series ahead, probably well ahead, of where you are. This is so that they will be here when you get here.

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