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AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Monday, December 05, 2005

Convey and Describe

Our class today was not about learning new stuff, it was about understanding the deeper concepts of what we learned before. Basically it was a day for enhancing our knowledge about the language of calculus.

We learned about the Extreme Value Theorem which states that if a function is continuous and is in a closed interval it has to( Mr. K repeatedly said it has to meaning its important) have a global max and min either in the critical points or the endpoints.

We also learned the 1st Derivative Test which is used to determine if a root of the derivative is a max or a min in the parent function. If the derivative is negative on the left and positive on the right of the root the then it is a local min if the left is positive and right is negative then it is a local max.

Critical points are on the parent function( max or min or where it is undefined)

Critical numbers are the zeros or root in the derivative function

The first example we had is to find the critical points of the given function.
f(x) = x^2 -4x +5
f'(x) = 2x-4
= 2(x-2)

the critical number is x = 2

to get the critical point we get the value of 2 in the parent function. Which is 1
therefore the critical point is (2,1)

we describe this by saying that by the derivative test that there is a min at 2 and the value is 1

Again all we talked about today wasn't something new. All we are learning now are concepts of what we discussed before. The point is we need to know how to convey and describe what is being asked and not just push some numbers in the paper.

The next scribe is.....

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