Ok, let me just say that I was somewhat scared when I walked in on Monday not because I didn't think I could do the work, but jsut because it was CALCULUS. However, I stressed myself out over nothing as usual.

To me, calculating the average speed was the easiest thing I've learned so far because it's just basic algebra with the slope formula. First, you identify the time you start and the time you end [t1, t2]. Each t value is the equivalent of a x value in the basic slope formula (y2 - y1)/(x2 - x1). Then you plug each t value in as your x in the equation given to describe the fall. The outputs are your y values. After plugging everything into your equation for slope, you get your average speed.

B-Rob stressed to us that we had to remember the Long way to find instantaneous speed (rate of change, definition of derivative), and I feel confident that I can do this becaus plugging into a formula is my thing. I like things thatare set in stone, so there's no question in my mind that I'll have a problem with this. You just take the limit as h goest to 0 of the function plus h minues the function all over h. So, this is it:

lim f(x + h) - f(x)
h-0 h

Then you just manipulate algebra to get the instantaneous speed or the derivative.

I really have a true understanding of everything, even after thirty-six formulas for derivatives were thrown on the board. For instance, the product rule states that when multiplying two things, you take one original times the derivative of the other and add that to the other switched up (this is better: (uv1 * vu1). I also understood how the quotient rule works and among other things (except, I keep forgetting the bottom of the quotient rule--my problem!).

The only things I'm unsure about do not actually involve doing the steps and formulas, just how to end the problem.
1. Like, after I take a derivative using the quotient rule and get a fraction, do I leave the bottom squared or foil it out?
2. Also, if I have a fractional exponent in the denominator, do I have to change it to a root and multiply by the conjugate to get rid of the radical on the bottom?
3. On the Section 2.3 sheet # 35, I didn't know what to do with three, so if anyone could help me, that would be great!
4. On the big packet (one with like everything), I didn't know how to do the ones where it started at a certain height. Could anyone explain to me an example (like #34?)? Thanks!

So overall, I think I had a good first week in Calculus. I learned a lot and am so psyched about the possiblity of getting college credit by taking the AP exam.

--Malerie