This week we went more in depth with derivatives and took our first quiz on them. I actually do not thing the concept is too hard but I still was a little skeptical about the quiz. I think I did well but on the other hand I could be totally wrong about everything.
I though lab 6 was pretty interesting. It was all about the correlation between the graphs of f(x) and f'(x). When the graph of f(x) is increasing the graph of f'(x) is above the x-axis. The opposite goes for when f(x) is decreasing at any point because the derivative will be below the x-axis. This also means that the minimum and maximum values of f(x) are the x intercepts on f'(x). I thought this was cool how it all works out. Math is awesome like that sometimes. When you finally see that one way of doing something, why it works, and how it all intertwines, it can be sort of eye-opening.
Lastly at the end of the week we learned some rules for finding the derivative without using a calculator. For example, the power rule helps a lot without having to plug in a long number into (f(x-h)-f(x))/h. These rules make finding the derivative more simple without huge calculations where there is more of a chance for error.
ALSO, funny side note. We had a cross country meet on Friday and this particular course had a lot of curves through the woods. Well, as I was running, a girl and I were rounding a corner and some coach yelled out something about running the tangent line. It was like she was saying instead of rounding the corner, we should take a straight line in order to run the shortest possible race. I already knew that it was something you should do but I though it was funny that the coach phrased it like that.