AP Calc: Week 5

I have heard many rumors the past few years about the dreaded derivatives and the horrors that accompany them. Well, now that they are here, I realize that they really aren't that bad. Especially when you learn the secret way to solve them, they could be worse. I still know how to do them both ways, but it is nice to know another way to do them so I know if I did them correctly.

However, I think that the most important thing that we learned this week was something from a fantastic vine.

"What is the derivative of a function??????"

"The derivative is the slope of the tangent at any point"

Fabulous words of wisdom right there.

Mostly what we worked on this week was doing calculations to find the derivative. We used this formula:

f(x)= lim (as h approaches 0) (f(x+h)-f(x))/h I have found it easiest to solve these problems when you do each portion one by one and simplify them as you go. You have to take x+h and plug it in for x in the function as the first step, and simplify it. It is also important to note that if you finish f(x+h) - f(x) and there isn't an H in each term, you are doing it wrong. You always have to make sure that there is an H in each term so that when you divide by H in the next step they cancel out.

So far I don't particularly mind solving for the derivative, but I certainly had a hard time graphing it in a gif!

Check out these beautiful words of wisdom here:

https://vine.co/v/hgp7dzpUOg7