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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.

Friday, October 14, 2005

Graphs And Derivative

In today's class, we had two questions on the board. the first question is about f' ( derivative function) and f ( original function). We had the graph of f', and we need to know where is f increasing, ( for looking for where f increasing or decreasing, we need to know the slope. Since a derivative is the slope of the tangent line at any point on the graph we choose (provided the derivative exists there, of course), positive slopes correspond to f ' > 0 , negative slopes correspond to f '< 0 and zero slops correspond to f'= 0

Where f have a horizontal tangent line means where are the zeros on f’, because when f have a horizontal tangent, the slop is 0, and zero slops corresponding to f’=0. Does f have any maxima or minima numbers? When we looking for if f have any maxima or minima number, first of all we looking for a function has to be a derivative function, and we look for the left or right side where x=0.because we know when x=0, that point is either max point or min point on the graph of f. The curve is increasing at the beginning and then reaches the zero and then decreasing, so we know, this point is a maximum point. The curve is decreasing and then reach the zero and then curve increasing again, and we can know this is the minimum point of f. If f(1)=0 is f(0) positive or negative? Since we know the graph of f, is increasing, reach the maximum point, and then decreasing , reach the minimum point and then increasing again. We know f’(1) is the maximum point of the graph f, if f(1)=0, and f(0) is the previous point of f(1), so, f(0) is a positive number

The second question we had today is draw a graph showing "mathmatical knowledge gained over the semester." Well, it can't be a straight line. And everyone knows that the line should be going up. Before we started our semester, we had some knowledge, so, when the line started, it's not zero or neither a negative number, and then the curve is going up, at the middle of the course we kind of stuck, some kind of suff we couldn't get it right way,because the course is going harder and harder. And before the test, the line is going slow or stop for a while. And then after, it's going up again, stuck, we need more time to study, or we have test again. .. and then it's over and over again till this semester is finish. So, basically, the curve is look like, start a postive number, concave up, concave down a little bit, and then stay a horizontal line. and then go over again because we started a new unit... ( I talked too much, bad explaination)Sorry!

P.S a critical pointis a point on the domain of a function where the derivative is infinite, underfined, or equal to zero. :P

And that's all for thday!

Next Scribe is Ara! :)

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