The calculus exam is coming up… Monday.  Looks like this will be a good opportunity to see if what I’ve learned is really sticking. So far I feel completely comfortable with what I’ve learned, and think I will do well. However there’s always the fear in the back of my mind that I’m missing something that I’m unaware of.

Derivatives, so far, are understandable. I realize it’s going to get harder and harder, but the homework assigned to us yesterday was a pretty easy thing to do, and I found that the application problems really helped me get a better grasp on why I would want to know the derivative.

For example, there was a problem asking how many cm^3 a 3 year old ram’s horn diameter would be. So all I had to do was plug in 3 to the given function and I easily arrived at my answer. What was cool, was the minute I realized that the derivative of the original function was the answer to the next question, which was asking me what the average rate of grown per year for that 3 year old ram would be. Then you just have to find the derivative of the function, plug 3 into that and you’re golden.

So it’s finally coming together for me that a derivative helps you find the instant rate of change for a specific year or specific degree, while if you wanted to find the average rate for something a whole, that would be the difference quotient. What I mean is, had the question asked me what the average rate of growth for all the ram’s possible ages would be, that would be a whole different process than just finding the average rate of growth per year for the 3 year old ram’s horn.

I don’t know if that made any sense to you guys, but it totally clicked here.

I’m hoping we eventually learn how to read a word problem and then formulate it into a function on our own… I’d like to know where they got the functions I got to work with in our homework this weekend. I think that would be useful, and I do imagine we will get there by the end of the semester and probably earlier than that.

As a semi-unrelated side note, I found this awesome Iphone app that lets you make your own meme posters… so now I can make my own math comics… excellent.  I have to find ways to keep it interesting, right?

But until I find a way to make math funny I am going to borrow one to close out my post.