Yes I assumed that the stores were located at the corners which is obviously wrong. However, how did yo ucome up with these 5 cases? Did you look at the initial equation

p1 + tau l x-z l < p2 + tau l y-z l

and assumed that first x > z, y > z and then x > z, y < z and so on?

The first case you wrote for exapmle, where p1 > p2 + tau (y-x) , what do you do check for the indiff point? Not sure I understand what I am supposed to check. If z = x the consumer will buy from y because it is cheeper but if z is slightly to the left of x he will still buy from y unless p1 + tau*(x-z) < p2 + tau*(y-z) ?

I did quick graphs in mspaint
in red, the graph of p1 + tau |x-z|, in blue p2 + tau |y-z|

left : p1 > p2 + tau |y-x|
center : p1 = p2 + tau |y-x|
right : |p1 - p2| < tau |y-x|

This should help you to see what happens.

Not a homework question.

If we assume that the rate of expansion in the universe is increasing does this also mean that the speed of light is increasing?

No. (Why would it?)

So what you're saying is that there exists a z like you described when red = blue in one point (i.e. in the graph to the right) which is exactly when

p1 + tau l x-z l = p2 + tau l y-z l

and assuming that z lies between x and y (we have that x < y in the first case) hence

p1 + tau (z-x) = p2 + tau (y-z)

=> ... => z = (x+y)/2 - (p1-p2)/2tau

then I proceed with the y < x case, is this right?

Calculus I help.

Hi everyone, In this problem I'm supposed to use the First Derivative Test to determine whether the function attain a local minimum or local maximum (or neither) at the given critical point.

y = (x^2)/(x+1), c=0

The answer is it has a local minimum but I'm keep getting maximum.

__________________________________________________ _______________
Here are the results I'm getting:

y' = (2x-(x^2)) / (x+1)^2
which equals x(2-x) / (x+1)^2
so the critical points are at x=0 x=2 and x=-1

so the intervals on the graph would be (-∞, -1) , (-1, 2) , (2, ∞)

f'(-2)=-8
f'(0)=0
F'(3)=-3/16

Which would mean c=0 is a local maximum wouldn't it?

(If you need me to give more detail I won't be back for an hour because I need to drive home from class)

First, your interval (-1,2) should be split at 0, your other CP.

Second, you never test f ' at the critical point (it is always 0 or undefined by definition), so you check a point in the interval.

So, check a point in (-1,0) and one in (0,2). If there is a local min @ x=0, you'll see that f ' is negative on (-1,0) and positive on (0,2).

[I'm assuming you took the derivative and did algebra correctly; I didn't check.]

I believe you made a mistake calculating the derivative.
y = (x^2)/(x+1), so y'=2x/(x+1)-(x^2)/((x+1)^2)=(2x(x+1)-(x^2))/((x+1)^2)
= x(x+2)/((x+1)^2).

wow, you are one dedicated poster man. you do some good work around here.

sweet thanks a lot man, this helps a lot.
(my calculus professor is chinese so I couldn't understand anything when she taught this)

Do you understand why f ' < 0 on (-1,0) and f ' > 0 on (0,2) means that there's a local min at 0? [my guess from your last post is no, but I may be wrong]

Thanks. I mentioned a while back that I miss teaching. This is a reasonable outlet for that.

Edit: i did it right on paper but typed it into the computer wrong

This isn't aimed specifically at you, but I'm going to rage for a minute at college kids who blame their lack of understanding on their Asian professors/GSIs. We've all had foreign professors who are a bit hard to understand. When those professors don't care (or seem to not care) about teaching (and we've all had them too), it makes it that much harder.

However, overall, students' study habits are atrocious, and their expectations from their professors are too high. I know that everyone's used to being spoonfed information by their high school teachers. When you get to college, you have to take charge of (and responsibility for) your own learning. Go to class if it helps you learn; if it doesn't, don't. But either way, you need to read the book (probably several times -- I'd recommend before lecture, then again after lecture at a MINIMUM), do practice problems, and learn the material. And if you're getting a half-assed understanding of it, get a tutor, join a study group, talk to older students, post in forums, something. Because the guy who's reading your application for med school, or the guy who's deciding whether to hire you or give you a scholarship -- he's not going to discount classes taught by Wang, Fu, and Zhang and give extra weight to those taught by Smith and Walker (who, incidentally, can also be atrocious teachers).

Just sayin'.

Wow, I feel stupid.

you sir are absolutely correct, I was working on this homework for 4 hours so i somehow missed this.

also thank you wyman I finally got the correct anwser

Don't think I'm blaming my professor because I agree with you on this.

I do study my math about 3 hours a day, and my calculus professor now Is the best math teacher I've had in years because she actually works out the problems, but she seriously has the thickest accent I have ever heard, and she talks extremely fast, and I still have trouble understanding her 7 weeks into the quarter, (and I've had a bunch of foreign professors).

(My text book didn't have any examples on that type of question so I had to go on from what I learned in class)

Although this is not a good spot to be in, there are still some alternatives, like Paul's Notes for calculus. He usually gives a fair number of examples, which seems to help a lot of people in calc/diffe.

I promise to study so long as you all promise not to use "trivial" every 3rd word while the whole classes has no idea whats going on. I kid you not, I had a professor who felt that any integral that mankind had ever solved was now "trivial" and was not worth any explanation.

I bet ever integral he showed you was trivial.

I also agree with Wyman. Everything you do in Undergraduate, especially those lower level courses that a lot of you are taking, has been done before. There are so many resources online, be it lectures, notes, solution manuals, examples, etc., that it's your own fault if you learned nothing during the semester.

Fair enough. If I use the word trivial, it's to illustrate that if you *don't* think it's trivial, then you are missing a concept.

By the way, to a mathematician or computer scientist (and I swear to god I had this conversation yesterday with a coworker after we had an algorithm for something and referred to it as "the dumb algorithm," even though it took a day to come up with), "trivial" really means "trivial, given sufficient thought about the problem." What I mean is, there's no sticking point here. Just crank through it using the machinery we've developed (whether that's integration by parts or whatever), and you'll get the answer, no problem.

If I'm saying that something requires little to no thought, I'll use the phrase "patently obvious" instead

Yesterday, one of my coworkers gave a research talk, and he showed a piece of our model that was evaluating something in an inefficient way, and he showed his improvement to it. I spent the next 10 minutes convincing myself that this was exactly the same setup as I'd seen in a computational geometry paper when I was a grad student, so I grabbed the paper from my bookshelves (I keep everything, I'm like a math hoarder) and in one day we'd gone from an O(n^2) algorithm to an O(n log n) algorithm (the dumb algorithm in my last post) to the O(n) algorithm, a slight adaptation of that in the paper.

So yes, random things you learn in grad school are useful in the applied world.

What if you use binomial distribution and find probability of 1, 2 and 3 of the 15 exceed 7.779?

is there a good matlab function for plotting phase diagrams of ODEs? i know ode45 can solve specific initial values but a problem wants me to show phase diagrams of a system of odes over the variation of a parameter and it seems like doing it by hand is going to be a pain. the system is

dx/dt = a + x^2 -xy
dy/dt = y^2 - x^2 - 1

where a is the parameter to be varied. i tried overlaying a lot of plots on a range of initial values but got tons of integration errors from ode45. the class very rarely asks for computer results and the professor hasn't given much guidance on it, i'm pretty familiar with matlab but never used it for phase plane diagrams.

I know very little about matlab, but a Google search yielded this:

http://www.polyx.com/_nelin/other%20...lot+cobweb.pdf