This week in AP-Calc, we learned about slope fields and separation of variables. A slope field is a graph of the slope at all the points on your interval. This will give you a general idea of what the original function will look like. These are not that hard since you plug in the points and graph the slope at that point. Sometimes, you might have to draw a slope field for an equation with both x and y. You still do the same thing and plug the point in and graph the slope at that point. Separation of variables is slightly harder. For that, you need to separate the variables from each other. you need to get all of the on kind of variable on one side, and the other variable on the other side. After that, you can anti-derive and get the original function, but don't forget about the +C. After that you can solve it explicitly or leave it. If you are given a point on the original function, this is the time to plug it in and solve for the +C.
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February 2018
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