The worksheet over derivitives and their graphs was easy enough, but we really didn't need the extra day on monday to work on it, I just worked on other homework. As for 4.3, I wasn't completely sure whagt a point of inflection was, and I'm still not certain (but I doubt myself with everything). It's just where the concavity changes right? The part about solving algebraicly where the graph was increasing/decreasing and concave up/down I would have never got if you hadn't explained it, really glad I didn't sleep though that part (I'm getting better about it!). Three day weekends are good, but are kind of moot when there's exams looming over the week afterwards.
Another test week, monday was the test so nothing to talk about there. Tuesday: finding extreme values, simple enough, but finding them algebraicly is still a bit fuzzy for me. I know to get the critical points, but how do you get the absolute extreema? My notes say to evaluate the function at those points, although I was very tired the day I took those notes. I guess I could just plug in those numbers. Wednsday was Mean Value Theorum which is basically the slope formula, which makes sense, because derivitives are the graph of the slope of the original graph; Thursday was more of that. Friday was connecting what we learned, which is a good way to end the week. Graphing f'(x) and f''(x) from the graph of f(x) takes a surprising amount of critical thinking. Basically it showed things like the extrema from the graph are the zeroes of the next graph down. Now I'm thinking of inception and how derivitives are like the different levels of dreams. Anyway, I liked ending the week on a sort of reflection, but perhaps it would be better to do reflections on mondays to keep this fresh in our heads. I also didn't like the
As far as anti-derivitives go, I think I get it, and the tangent line is just the derivitive of the equation right? I really have no problem with sketching f from f' as the book calls it, although when I graph the f' to f, I seem to make silly mistakes. The chapter 3 review was fairly easy, and only a few problems really stuck out as difficult to me. The derivitives of e^u and ln(u) are simple enough, but the derivitive of a^u I will have to write down. I'll also have to write down the derivitives of sin cos and tan, and sin^-1 cos^-1 and tan^-1. I think I know how to do higher order derivitives, but I'm doubting myself again. Looking back on limits, I remembered that I need to know limit of x to infinity of sinx/x = 0 and limit of x to 0 of sinx/x = 1. I have a feeling that will come back on the test.
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