This week we learned how to find the derivative of more complex functions and the antiderivative. I found it to be fairly easy, sometimes it was scary to look at but once you break down the problem it's not too bad. The hardest part for me at first was when we switched to antiderivatives. I obviously remembered how to find the antiderivative but it took some practice before I was able to do it quickly again. The other thing I struggled with was figuring out what the u value would be. Once I understood the chain rule better and realized it was the inside of the composite function then it helped me be able to solve the questions. On the quiz I messed up by forgetting a negative when I was finding the derivative of sec(x) :((. The derivative of sec(x) was given to us in our notes but I forgot to put a few of those on my cardstock paper which would have made that question a piece of cake. I think I did pretty good on the rest of the quiz, I felt confident about it and was able to finish it pretty quickly and look over my answers (and I still missed my negative mistake). Cresswell said that each question was worth multiple points so hopefully me missing that question doesn't result in a 75%.
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This week we learned how to take the derivative of functions that had multiplication or division in them, antiderivatives, and the derivatives of trig functions. It was fairly easy, probably the worst part about it was the length of my work for certain problems. I understood the concept and feel confident about the quiz but also know the exact question I messed up on and we haven't even gotten our scores. The question I messed up was the product rule for one of the trig functions. I forgot to apply the product rule for some reason, so I didn't do the (u)(v')+(v)(u'). Depending on how many points I'll get docked for that I may retake this quiz because I know that I could easily score 100% on it. I've been able to calculate the problems without the calculator. I will occasionally double check it by graphing if I am unsure about that problem but I felt pretty good about the homework problems for the most part and felt no need to do that. I think next week I need to improve on staying on top of the homework assignments, I did a little bit of cramming on Thursday night, which is probably why I messed up the trig function on the quiz.
This week we learned about how to graph derivatives without a calculator, how to know when derivatives will fail, and the different rules of derivatives that allow us to write/find the derivative without using the four step process. I really struggled with the concept of tangent and normal lines. For some reason I had a hard time figuring out how to write the equation for them. After blindly doing a homework question about tangent lines I thought I came to a an answer but all I really found was the slope. After talking with some other people they explained to me how to do this kind of problem and I thought I got it but when I tried to do it later on my own I was lost again. I had just memorized the steps instead of actually understanding the "why" behind each step. So I took a closer look and realized that once you find the slope you want to find the y-value at the given x-value and then plug all those numbers into the y=mx+b formula to find the y-intercept and then rewrite the equation. You want to find the slope at the tangent so that's why you plug it into the derivative first. But next you want to find the values at the actual equation not the derivative. This week we learned about derivatives and the first thing we did to help us understand was create graphs on gifsmos. It represented how the slope of a line got more accurate the closer the two points got together which turned it from a secant line into a tangent line. The activity at the beginning of the hour helped me to understand that concept. I struggled a little bit at first because I just didn't know where to start. Talking with my classmates definitely helped me get on the right track. I was almost finished with my first graph but was stumped on how to get the sliders to move so I asked Mr. Cresswell who helped explain things. The first graph required a stationary point with one slider number f(a) and the second graph both sliders numbers moved by adding f(b) and slope formula m=(f(a)-f(b))/(a-b), the avg rate of change. For the third graph I kept everything the same expect for the original f(x)=.5x^2 function. I changed it to f(x)=sinx^2 and it still worked because of the f(a) an f(b) slider points.
Unfortunately this week I got a C on my quiz and the frustrating thing but also the reassuring thing is that it was all simple mistakes. Fortunately, I get to retake this quiz because my mistakes were forgetting to label with the limit notation - which I did in all my homework but for some reason didn't do it on the quiz ? I don't know why. And then my other slip-up was on the C^3 because the limit approached infinity but super slowly and I didn't realize because I went through it too quickly. Good news is, I understand everything I did wrong on the quiz now, even the parts that weren't simple mistakes, I figured those out and feel confident about retaking the quiz. I felt very prepared for the test on Friday too, I studied Thursday night (and I have never ever studied for a math test) so I wasn't worried. However, there was some stuff about natural logarithms and fog(x) problems that we have not learned about and were stuff from last year that I didn't realize I would need to review. I'm hoping I still did okay besides these two problems but kicking myself in the butt for not reviewing better. You learn the most from your failures though! How does what I learned connect to previous topics and what might it be leading into |
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March 2017
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