Week #5

Quiz number three, as expected, had a mixture of results. Many of you are well prepared for calculus, but others remain unsure of pre-calculus concepts covered on this quiz. Please, if you need help with any pre-calculus topics, I'd really welcome your questions. So, please ask during class or during office hours.

Also, I will try to run weekly anonymous surveys, please consider participating each week.

For those who want extra credit, do problems 1 and 2 on page 125. It's due Monday, October 10 October 04, 2004 at 8:30 a.m.. It's worth 10 points total, and I will just add this to your quiz grades. Even if you're getting perfect scores on all quizzes so far, you should still do this assignment; sort of like an insurance policy. Oh, as usual, you must show all work on this extra credit. I know they're tough problems, but I think many of you can do it. For those that can't, I'll give other extra credits. Everyone, eventually, will find something. Answers to the bonus questions will be posted, in jpeg format, on the right sidebar.

You should have the definition (the one I gave in class) of the derivative down and be able to manipulate your way towards finding the derivatives of any of the following functions: polynomial, rational, root, or combinations and/or compositions of these. Yes, the manipulation may be tough and lengthy. Also, you should have a good sense of what information this derived function (hence, the name derivative) gives about the original function. Two examples of using the derivative were given: instantaneous velocity, and equations of tangent lines at a given point on a function.

Definitions are necessary, but this week we will discuss rules for finding the derivative. All rules given will follow directly from the definition of the derivative.

For those interested in Mathematica, here's the command for taking the derivative of f(x) = 3x² - 2x +7, with respect to x is:

D[3x^2 - 2x + 7, x]

The first part is the function, the second part is the variable that we are differentiating.

I'm not trying to push Mathematica, but the school has a site license for those interested in using it on the school's computers (I believe it's the 3100 labs). Certainly, other software for taking derivatives exists and many calculators are quite capable of taking derivatives. On the TI-89, for example, the command for taking the derivative of f(x) = 3x² - 2x +7, with respect to x is:

d(3x^2 - 2x + 7, x)

I should be getting a copy of MATLAB this week for evaluation, and I will soon post information for those interested. ECC does not have a site license for MATLAB, but for those of you planning on attending NJIT, I'd strongly suggest that you at least familiarize yourself with MATLAB or Mathematica. Both are offered to students at a hefty discount.

On a side note, last week I mentioned Genghis Khan in passing. Certainly, he is a great legend, mostly known for his conquest that extended from the Korean Peninsula all the way to Europe. And yes, like any great leader, he's an interesting character. Why did I mention him? First the arrow (Mongols' weapon of choice), then it's power, used wisely to conquer, in fact he controlled the greatest empire ever. His conquest was fleeting though, all are, but many of the real achievements remain intact. Most know of his ability to subjugate, but it's the softness of his people's hearts that remain his greatest legacy.