This week in AP Calc, we primarily discussed derivatives. I find derivatives pretty easy to grasp especially since we had all of the practice with limits and continuity already. When we were given the function representing the derivative of f with respect to x: f'(x) = lim f(x+h) - f(x) h->0 h I found everything else to become a lot simpler. Along with this function, we received the 4 Step Method for solving for the derivative. I think knowing step-by-step what you're supposed to do makes solving these types of problems a lot easier, and then makes the problem only dependent on our basic algebra skills. What I kind of struggled with at first was remembering these little tricks we learned throughout algebra over the past few years. Step one of the process, which is to find f(x+h) is easy to go about doing and so is Step two, which is to write f(x+h) - f(x) and simplify. Simplifying is easy, but on specific equations like: f(x) = √(x−1) it was somewhat harder for me to remember to multiply by the conjugate, and small things like that when simplifying. (Top right) | I also think that Lab 6 was helpful in better understanding derivatives. When I was first doing the lab, I found it pretty easy. Making a quartic function for the four zeros was pretty easy. What I struggled with at first was just reading the directions carefully, especially specific directions like "over what intervals does the graph of f appear to be rising as you move from left to right". Once I noticed the relationship between the rising intervals of f(x) and the points above the x-axis of f'(x) and the falling intervals of f(x) and the points below the x-axis of f'(x), it became a lot easier. Then I made the connection between the x-values of the maxima and minima points of f(x) and the zeros of f'(x). (I've attached a link below to a graph showing this). After coming to this realization the whole assignment got a lot easier. Graph |
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February 2015
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