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It is not a coincidence! On curious patterns in calculus optimization problems. (English) Zbl 1380.97008

Summary: In the first semester calculus course, we learn how to solve optimization problems such as maximizing the volume of a box or a can given its surface area, i.e., the amount of material, or minimizing the surface area given the desired volume. Whether you are a student or a teacher, have you ever wished you knew the answer to a problem after one glance at it, without doing long calculations? The patterns shown and explained below will enable you to do it for a few “standard” problems, but more excitingly, they will illustrate some very beautiful problem solving techniques and give insights into how different areas of mathematics are connected.

MSC:

97N60 Mathematical programming (educational aspects)
97I40 Differential calculus (educational aspects)
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