Over the past couple of weeks I have began to notice everything that we have learned up until this point in the class is starting to come together and it is making more sense because we get to see the whole reason behind learning derivatives. These past couple weeks, we have been learning about the topics of optimization and related rates. At first, it was a little bit difficult to understand these topics, but after some practice, I began comprehending the ideas of the topics more in depth and they overall became easier for me to solve. Optimization and Related Rates are very similar topics but are different in their own ways. Optimization in simplest form is the mathematical steps to figuring the most effective way to do something using the least amount of resources or the most effective use of a situation using mathematical equations like area, trigonometry, or Pythagorean Theorem. Some examples of the optimization problems that we were working on are the open top box problem, the paint can problem, the inscribed rectangle problem, and the boat problem. The boat problem consists of a boat that is a certain distance from shore and they want to reach a point up the beach. We used optimization to find the most optimum place to land on the beach to make the trip in the shortest amount of time. Related Rates deals more with a situation that is already happening and you are required to calculate how fast a certain value is changing using mathematical equations like area, trigonometry, or Pythagorean Theorem.
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January 2018
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