Second to last...

It's so close guys :-D. All of our hard work and doing these blogs and doing the APs will finally be paid off this Wednesday, the day of our AP. :-)

So, on the final blog before the AP, what should I post about? Well...hm.

I know, I'll do like a final study guide type ordeal. I'll cover as much as I can remember and put it in one short post.

1. Average rate of change - this is simple, don't confuse this with average value or rate of change. This is just a slope. f(b)-f(a)/(b-a).

2. Rate of change - this is simply a derivative! plug in an x value and get a slope out, your answer

3. Average value - this is 1/(b-a) times the integral from a to b of f(x). This is just an integral times by 1/(b-a).

4. Maximums, minimums, critical values, increasing, decreasing - all this crap is related to first derivative test. it's simple. you take the derivative, set equal to 0, solve for x. Set up some intervals using these numbers. Plug in numbers and test your intervals. pos to neg is a min. neg to pos is a max. pos = increasing, neg = decreasing. simple stuff. remember it.

5. Point of inflection, concave up, concave down - it's the second derivative test. set up intervals, if the intervals change signs, it is a point of inflection there. also, if its negative, that interval is concave down, positive is concave up.

6. Slope of a normal line - take derivative, plug in x. get a slope. however, make sure you use the negative reciprocal of the slope (normal means perpendicular to). use point-slope formula.

7. Equation of a tangent line - take derivative, plug in x. get a slope, use point-slope formula.

8. linearization - do an equation of a tangent line. then plug in the decimal number they gave you. then find y.

9. finite limits - just plug in the number and get a value. try to factor out before hand if possible.

10. infinite limits - degreetop > degreebottom = infinity, degreetop < degreebottom = 0. degreetop = degreebottom = degreetop/degreebottom

11. Vertical asymptote - set bottom = to 0. make sure you have factored and canceled anything beforehand.

12. Removables - factor top and bottom of the fraction. make cancellations. if something canceled, that factor is a removable.

13. Horizontal asymptote - same as infinite limits. see 10.

14. Area if only one equation is given - integrate the equation of and plug in two x values

15. Area between two equations - find your bounds, then do the integral from a to b (your bounds) of top-bottom

16. Volume by disks - find bounds, then do pi times integral from a to b of (top-bottom)^2

17. Volume by washers - (has a hole in the graph when you rotate about an axis) find bounds, then do pi times the integral from a to b of (top)^2 - (bottom)^2.

18. Cross sections - use the area of the cross section, and integrate that, but plug in your normal top-bottom for the variable. for instance, s^2 is a square crosssection. so you would do integral of s^2 which is (top-bottom)^2.

Enjoy.

:-)