Post Number Three

So, the third week in calculus has passed and i feel a little better though at the beginning of the week i was pretty much ready to get murdered. The first two days we reviewed derivatives and limits and everything that was going to be on the test Wednesday. Of course I was at our infamous study group sessions, though i still don't think i did well on the test at all. I knew all the formulas, i just felt i couldn't apply them to the problems. When i practiced problems studying i did not have any problems with them but i drew a blank when the test came around. I find the arc trig formulas the easiest.

Thursday and Friday we learned new things which i actually caught onto right away. I don't care how much ricky makes fun of me atleast i understand something :) First, we learned calculus graph vocabulary which is fairly simple:
Increasing-slope going up; original
Decreasing-slope going down; original
Positive Slope- first derivative (above)
Negative Slope- first derivative (below)
Concave Up- second derivative (bowl)
Concave down- 2nd derivative (umbrella)
Horizontal Tangent
Slope=0
Derivative above axis
Derivative below axis
Zero of derivative
Maximum-original
Minimum-orignial
Extrema

If the slope is postive it is increasing while if the slope is negative the graph is decreasing.

Friday we then learned the first derivative test, step by step.
1. Take a derivative
after this you must check for pts of discontinuitys
2. Set the derivative equal to zero.
3. Solve for x to find max, mins, horizontal tangents, and extrema (critical points)
4. Set up intervals using step 3.
5. Plug in first derivative (hence that this is called FIRST derivative test)
6. To find an absolute max/min plug values from #5 into original function
Check endpoints!

All of this is pretty simple to me, especially since Mrs. Robinson elaborately showed us the graphs on the first day and tediously taught us how to read the graph. Just remember, drawing a picture always helps :)