Hello math world! I apologize for my absence throughout Thanksgiving break. Many new things are starting to go on in AP calculus. We learned about optimization this last week and had a quiz on it. We also started to learn about related rates near the end of the week. Optimization is when you want to maximize or minimize a certain value. These sections fall under the applications of Derivatives section because they force you to use Derivatives in order to optimize or relate your rates. Unfortunately I couldn't be at school 3/5 days this week, so I was only able to start taking the quiz today. I'm finding it much harder to understand than things we learned in the first trimester of class. This weekend I'm going to try and watch a few videos in order to grasp the concept more. An example of an optimization problem is if you have 30 square inches of text on a paper, and you have margins that are 2 & 3 inch long, how can you minute the amount of paper used (what are the dimensions of the paper). You want to set up two equations: x×y=30 and (x+4)(y+6)= Area of full paper. Now, you want to be able to isolate one variable, so you can find by using the first equation that 30/y=x. Now after this step you plug 30/y back into the second equation for x, and you then multiply out your equation, take the derivative, and find the zeroes of that derivative. These zeroes will give you the minimization of y, and you go and plug y back in to the original equations to find the dimensions of the paper. These problems are much more time consuming than problems strictly containing derivative usage. I hope that throughout next week I can get caught back up in the work and have a very successful trimester. Go math!
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