Merry Christmas and Happy Holidays to all blog viewers. In the previous week we took the test over optimization, related rates, and the non calculator curve sketching. I did very well on the test and aced it! None of the questions were too hard. The related rates that I struggled on the week before the test was cleared up by Mr. Cresswell and videos on YouTube. Also, the questions on the test were much easier than questions on the quizzes. One of the questions I vividly remember from the test involved related rates and the volume of a cylinder. You also had to relate this go a rectangle where x was the circumference of the cone and y was the height. You wanted to know the rate at which the volume changed at a certain length of the circumference x. You can find this setting the radius equal to x/(2pi). Next you plug that back into the volume equation after you take the derivative of the equation. You then are able to find your rate. It's much simpler when you have a picture to follow along with. Thank you for viewing my blog and have a happy holiday. Go math!
Hello all blog viewers! This week in AP calculus I accomplished many things! On Monday I finished the optimization quiz and did very well on it. I got an 18/19 on the quiz and feel very confident for the test that we have coming up on Monday. Since I missed so much school the previous week, I had to go right into the related rates quiz on Tuesday after finishing up optimization. I definitely struggled with the quiz, but I ended up being able to figure out all of the problems after some thinking. One of the problems I struggled with most was a problem involving water dripping out of cone cup. I ended up figuring out that you have to get rid of one of the variables by using similar triangles and plugging all of the numbers back in. Out of all of the tests we have taken in AP calculus, I feel the least confident going into this one. This is because there are so many different types of questions that could be tested on related rates and optimization that it is hard to prepare for it. I look forward to seeing my score on the test so I can see how much I've learned in the second trimester. Go math!
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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