So this week we started to learn about related rates problems. And like Mr. Cresswell, I really enjoy doing these problems. This is about the exact opposite way I feel about optimization. I think the main reason that I like these problems is the fact that they involve implicit differentiation, which is like my ultimate favorite math thing to do. Another cool thing about related rates problems is the fact they look at sound incredibly hard, but really, they are just a few simple steps to figure out. Basically, related rates problems involve:
1. coming up with an equation for a picture
2. IMPLICIT DIFFERENTIATION! YAY!
3. plugging the stuff in that you already know
The only slightly difficult part to these problems may be the figuring out what the problem says and how it relates to the variables in your derivative. But even then, you could use a process of elimination. I find that what helps me to figure out the problem the most is the simplest/hidden step: writing down everything that the problem tells you or that you can easily find out. Even though people might think that this step is not necessary or stupid, it really isn't. It is a great way to organize ideas and it lets you sit down and really think what each thing means. Then the last step is even easier because all you have to do is plug stuff in, and without even thinking about it.
I also want to take a minute to talk about the quiz over optimization that we took this week. I thought it was pretty horrible just because I really do not like optimization. I think that I got the answers, but the process became kind of difficult. I would write the equation and graph it to find the minimum or maximum, and I knew that this was the answer. But then, after I took the derivative of the equation and graphed it to find the zeros, I would discover that the answer was different. I don't know if I just took the derivative wrong or what, but it seemed to happen every single problem. This was frustrating because I wanted to make sure I had the right derivative. I also would start to second guess all of my work and that was not fun. Anyways, let's not do any more optimization please.
1. coming up with an equation for a picture
2. IMPLICIT DIFFERENTIATION! YAY!
3. plugging the stuff in that you already know
The only slightly difficult part to these problems may be the figuring out what the problem says and how it relates to the variables in your derivative. But even then, you could use a process of elimination. I find that what helps me to figure out the problem the most is the simplest/hidden step: writing down everything that the problem tells you or that you can easily find out. Even though people might think that this step is not necessary or stupid, it really isn't. It is a great way to organize ideas and it lets you sit down and really think what each thing means. Then the last step is even easier because all you have to do is plug stuff in, and without even thinking about it.
I also want to take a minute to talk about the quiz over optimization that we took this week. I thought it was pretty horrible just because I really do not like optimization. I think that I got the answers, but the process became kind of difficult. I would write the equation and graph it to find the minimum or maximum, and I knew that this was the answer. But then, after I took the derivative of the equation and graphed it to find the zeros, I would discover that the answer was different. I don't know if I just took the derivative wrong or what, but it seemed to happen every single problem. This was frustrating because I wanted to make sure I had the right derivative. I also would start to second guess all of my work and that was not fun. Anyways, let's not do any more optimization please.