Tuesday, November 27, 2007

Scribe #5 out of A LOT!

Today's amazing class started off with a bit of side-tracking. Mr. K. introduced us to a couple anecdotes that will be helpful to everyone in their overall learning skills. Now of course Mr. K. got them from a source that I am quite lazy enough not to discover... but they were:
LEVELS OF LEARNING (Bloom's Taxonomy)
Basically describes the different ways we can learn. They are Remember, Understand, Apply, Analyze, Evaluate, and Create. When we begin to learn in elementary, we start at the beginning and eventually climb up the levels of learning. Currently we are at the levels of Analyze and Evaluate, which still require all the others, and use them in class everyday.
Shows the different media (or methods) from which one can learn and the percentage of that knowledge that one would retain from each method. These methods are (in order):Lectures, Reading, Audio-Visual, Demonstrations, Discussions, Practicing by Doing, and Teaching. It turns out we only retain about 5% of knowledge from Lectures and a whopping 90% from teaching... that's a huge gap!
So in conclusion, Mr. K. told us that when we do our DEV (Developing Expert Voices projects)
, we are combining the Create and Teaching methods. That is one heck of a lot of learning that we do!!!

But now I will jump into the actual lesson of the day...

Well, we first did a quick review of the First Derivative Test, which is:
Next, Mr. K. introduced, the Second Derivative Test, which goes as follows:
We then jumped into some sample questions using this test. These can be seen on the slides for today's class. As well, you can click on the links underneath the definition of the tests on the green pages for more practice problems.

Next Mr. K. showed us a little loop-hole... It is thought that when the second derivative (ƒ''(x)) is equal to 0 (zero), there is a point of inflection on the parent function right??? The thing is, it might not be. It may in fact be only a candidate for the point of inflection. Then we must test the concavity on either side of this point (whether ƒ'' is positive or negative). If the concavity is different on each siide, it is a point of inflection, but if it is the same on both sides, the point is not a point of inflection, it is a local extreme that is relatively flat in a certain interval. AN EXAMPLE OF THIS IS THE FUNCTION ƒ(x)=x^4

We then continued with practice problems (which can be seen on the slides; link is above) until the end of class.

Quick thing to add to our understanding of these tests:

First Derivative Test: Interval test; find the candidates for global extrema and check the intervals on each side of them to prove they are in fact extrema.

Second Derivative Test: Point test; find candidates of global extrema and find the concavity of the parent function at each candidate.

Mr. K. has said, that one is not necessarily better than the other, they are just DIFFERENT... meaning in different situations, different tests will be better to use. (I like the Second one better)

That just about wraps up my Scribe for the evening...


Next Scribe is.......

1 comment:

Kara said...

I am also a fan of the second derivative test over the first derivative test but have definitely found that knowing how to properly use both of these tests is important for not only this but also other topics down the line. Great work on the post!!

Kara S. (Mentor)
University of Regina