This week was all about the chain rule. I was very confused the first day we learned it but the days after that I was able to see more clearly how it works. I honestly am still slightly confused because when doing the mini quiz I kind of forgot a lot of simple rules to follow, although I did end up getting a good score. You would think that the finding anti derivatives using the chain rule would be harder but I actually though it was the easiest question on the quiz. I think the main reason why derivatives can be confusing is because when you need to use these crazy rules in order to figure out a problem you forget why you are doing this to begin with. For me I tend to do this thing in math where I just concentrate on trying to solve one problem that I forget why I’m doing it in the first place. It all makes sense to me right now, I just think it is a common thing for people to fall into doing math without any purpose. In itself derivatives are pretty simple, there are just a ton of different ways to solve them and that’s why it makes calculus a little difficult. You have to concentrate on what rule you need to use for each problem.
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This week we dove further into rules for derivatives. We learned the product rule, quotient rule, and others in order to calculate the derivative faster. We also were shown rules for trig functions which in my opinion were easier to use than the other rules. This whole lesson leading up to the quiz was actually pretty easy in my opinion. As long as you know the specific rules it is pretty simple to figure out any problem. Especially when you have functions that are long and to the seventh power for example. It makes life a little easier when you do not have to use f(x+h) – f(x)/h for problems such as those. We also continued doing anti derivatives and finding higher order derivatives which are both super simple as well. This week we had a couple different homework assignments and worksheets but I was able to get everything done fast and I knew how to do a lot of what was on there. I am glad we are doing something fairly easy because it makes me not have to worry so much over this class and can concentrate on fun things like college applications. Im kidding obviously. In other exciting calc news, I redid my sheet of cardstock for tests and it looks nice. That is all. This week we went more in depth with derivatives and took our first quiz on them. I actually do not thing the concept is too hard but I still was a little skeptical about the quiz. I think I did well but on the other hand I could be totally wrong about everything. I though lab 6 was pretty interesting. It was all about the correlation between the graphs of f(x) and f'(x). When the graph of f(x) is increasing the graph of f'(x) is above the x-axis. The opposite goes for when f(x) is decreasing at any point because the derivative will be below the x-axis. This also means that the minimum and maximum values of f(x) are the x intercepts on f'(x). I thought this was cool how it all works out. Math is awesome like that sometimes. When you finally see that one way of doing something, why it works, and how it all intertwines, it can be sort of eye-opening. Lastly at the end of the week we learned some rules for finding the derivative without using a calculator. For example, the power rule helps a lot without having to plug in a long number into (f(x-h)-f(x))/h. These rules make finding the derivative more simple without huge calculations where there is more of a chance for error. ALSO, funny side note. We had a cross country meet on Friday and this particular course had a lot of curves through the woods. Well, as I was running, a girl and I were rounding a corner and some coach yelled out something about running the tangent line. It was like she was saying instead of rounding the corner, we should take a straight line in order to run the shortest possible race. I already knew that it was something you should do but I though it was funny that the coach phrased it like that. This week was all about all about gifs and derivatives. We used desmos to create graphs that relate to the derivative unit in class. I honestly started out really confused trying to make the graphs. I understood the concept and why we were doing it in order to learn about secant and tangent lines in relation to slope. However, I was very unsure how to actually create the graphs. I was able to figure out the first one in class, with help, but on the on the second one I was totally lost. I eventually figured out how to do it by evaluating each formula and how it related to the graph as a whole. I'm glad I figured it out on my own so I can understand the concept better. The first graph depicts the slope of the tangent line as it gets closer to the point (2,2) on the graph f(x)=.5x^2. The second is relatively the same but instead of a stationary point, it uses points f(a) and f(b). On the third i switched f(x) to equal the sec(x) mostly because I thought it would look cool (it does). It is also interesting to watch the points as they jump to different infinities.
The rest of the week we spent time doing lessons on derivatives. They make a lot of sense to me now that I understand how they are supposed to work. Last year I remember discussing them and doing related problems but I never knew why or what they were for. It is nice being able to connect everything and know the background of the formula. This week we had our first chapter test over limits and I thought I did fairly well. I was confident in many of my answers accept the salt and pepper function which I wasn't able to answer but that is alright. I understand the basis of how they work I just could not find the exact equations that would make the statement true. I do enjoy those problems though. I like that satisfying feeling of figuring out a problem such as these. This type of math is why I enjoy it. Sometimes it can be like solving one giant puzzle and once you finally figure it out you are filled with relief and a sense of pride. The salt and pepper functions are a little bit like that which makes them enjoyable. I also am really enjoying the mental math exercises we do every day. Those are also really fun and kind of like a game. I like thinking out things in my head like that. I like it so much that sometimes when I’m bored from running long distances I’ll start doing my times table and see how far I can get while still keeping track of all the numbers to pass time. I’m such a nerd. |
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Haley FoxJust a high schooler trying to learn and blog. Archives
March 2017
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