by collegebookworm » Sat Oct 27, 2007 9:48 pm
We're searching in the range [unparseable or potentially dangerous latex formula], because those are the x-value endpoints of the closed area between [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]. I'll define a new function, [unparseable or potentially dangerous latex formula] to make this optimization easier.
The area of a rectangle enclosed in the region is [unparseable or potentially dangerous latex formula]. To optimize the problem, one should look at the area of rectangles when x and y are at their endpoints and at their critical points.
The critical points of function A are where the derivative equals zero, so we have: [unparseable or potentially dangerous latex formula]. When the derivative is zero, [unparseable or potentially dangerous latex formula].
The value of A at the the endpoints and critical points are:
[unparseable or potentially dangerous latex formula]
Notice how the area for the endpoints is zero, which we would expect since the y-values at those x-values are zero. Notice too how the area for the [unparseable or potentially dangerous latex formula] x-value is exactly the negative of the area for the [unparseable or potentially dangerous latex formula] x-value, because [unparseable or potentially dangerous latex formula] is even. Thus, we can calculate the area at all more points on the curve, but we can safely say that the largest area is about [unparseable or potentially dangerous latex formula]
(NS/CA/MA/CS/SC) "**" indicates TMSCA State
08 HI(LO): 142?-**(88-D2)/224-D2(17x-**)/320-D2(202-**)/248?-D2(206-**)/210-D2(17x-NovA+?)
08 D2: 88/224/320/210/248
Next meet: Texas Tech (Region, 4/11-12)