Well it is that time again, a chapter test is coming up. First of all, I just want to say that I am incredibly happy that it got moved to Monday, just because it has been a very long time since we went over what we learned at the beginning of this chapter. I realized this when I started doing the assignment and I noticed that I basically forgot everything about minimums and maximums and inflections points.
I don't know why but I have always seemed to struggle with comparing f(x), f'(x) and f''(x) and using them to figure out mins and maxes etc. Not only do I have to really sit there and think about it a lot, but I also have to spend a ton of time working on them. I think the problem that I had most trouble with was a problem where the first derivative was really complicated, which means that it would be incredibly difficult to take the second derivative. This was really confusing because I was taught how to find multiple things with the second derivative, and instead I had to find them using the first. But, luckily, you said that there wouldn't be any like that on the test so hopefully I don't have anything to worry about!
I think that I feel pretty confident with my optimization and related rates skills. At first, I did kind of struggle with the optimization problems, but I think that working with the related rates problems has helped me to better understand optimization problems. Even though they are different, they have a few similar aspects. For example, the steps to each problem are quite similar. Both need images of the situation drawn. They also include finding equations to go with the problem and using substitution. I personally like doing related rates problems better because, as I said before, they use implicit differentiation.
Differentials are also quite fun to do considering the fact that we already basically know how to do them but with one extra step. All they are is finding the derivative and multiplying both sides by dx. It is simple problems like these that I am quite thankful for to see on a test or quiz.
I don't know why but I have always seemed to struggle with comparing f(x), f'(x) and f''(x) and using them to figure out mins and maxes etc. Not only do I have to really sit there and think about it a lot, but I also have to spend a ton of time working on them. I think the problem that I had most trouble with was a problem where the first derivative was really complicated, which means that it would be incredibly difficult to take the second derivative. This was really confusing because I was taught how to find multiple things with the second derivative, and instead I had to find them using the first. But, luckily, you said that there wouldn't be any like that on the test so hopefully I don't have anything to worry about!
I think that I feel pretty confident with my optimization and related rates skills. At first, I did kind of struggle with the optimization problems, but I think that working with the related rates problems has helped me to better understand optimization problems. Even though they are different, they have a few similar aspects. For example, the steps to each problem are quite similar. Both need images of the situation drawn. They also include finding equations to go with the problem and using substitution. I personally like doing related rates problems better because, as I said before, they use implicit differentiation.
Differentials are also quite fun to do considering the fact that we already basically know how to do them but with one extra step. All they are is finding the derivative and multiplying both sides by dx. It is simple problems like these that I am quite thankful for to see on a test or quiz.