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I liked this problem and throughout the whole middle part I thought I was doing it wrong and no way would I get the right answer but then everything worked out and cleaned up really nicely. It was a satisfying problem

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I thought it was interesting to see this problem on a graph. I'm not completely sure if I got it right, but I tried to use correct notion.

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I just want to make sure that this is the correct notation.

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I felt pretty confident in the problem, it was fairly straight forward to solve. Although my work is kind of all over the place.

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This is the one I was most confused on. After looking at my notes from last year I pretty easily understood how to do it, but I'm confused on the why and what it means

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gebra trouble on the second part of this problem, I was able to confirm on Wolfram that I got the correvt answer for the derivative, and going through my steps I couldnt find where i went wrong.