This week we dove into chapter 3 and derivatives. First we learned what a derivative was. It's the slope of any given on a function. We learned about taking the slope of tangent lines. We learned that to find the derivative at a point you have to use the limit as h approaches 0 of f(a+h)-f(a)/h, where a is any given x value. To find the derivative of a function you have to use the limit as h approaches 0 of f(x+h)-f(x)/h. We did a lot or practice with this and we did several worksheets to go with it too. There was a four step process to go along with this. First find f(x+h). Then write f(x+h)-f(x) and simplify. Next find f(x+h)-f(x)/h and simplify. Finally find the limit as h approaches 0 of f(x+h)-f(x)/h. That will give you the derivative of the function. This week I understood pretty much everything. At first things were a little sketchy but once I figured it all out it got a lot easier. One thing I struggled with a little bit was understanding the graphs of the derivatives. It was hard to understand what they meant but after awhile I started to figure it out. Also we had to cube x+h quite a few times, and luckily Ishan reminded me and Kiegan of Pascal's triangle and that made it much easier to do the cubing. I think that this week was pretty important because we will probably have to use derivatives in the future. It's kind of a calculus thing. And limits came up again this chapter so I'm starting to see how all the things we learn will kind of connect. Math class is kind of like a toolbox that we keep adding tools to every week.
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