Your teacher is unambiguously wrong. He probably has an undergrad in math and thinks he's pretty hot shit 8)

I mean, I get what he's saying about it becoming more negative, but that's just not how it's described in any math class I or my wife (who is a math professor) has ever taken.

His second misstep, even if he's 100% right about the math, was not awarding you the points when you brought it up. The point of the question is to figure out if you get the concept of non linear derivative, which you clearly do. He's an ass for not giving you those points when you made your case.

C'est la vie I guess... I'd give you the points, but welcome to planet earth.

[Edited by - Pete Michaud on May 26, 2010 10:02:26 AM]

Its clearly decreasing at an increasing rate.

First we agree that its decreasing.

Now looking at quadrant I, we see that it either blows up at t->INF, or
it reaches an horizontal asymptote. Either case the derivative at time t = x,
is positive and thus increasing. You can even take a secant line, with small
epsilon, and see that slope will be increasing.

Quote: Original post by Hedos

Quote: Original post by nullsquared
Rate of change only includes a sign to show direction; as such, if a rate of change is increasing, then it could be getting more positive (numerically increasing) OR more negative (numerically decreasing), and if a rate of change is decreasing, then it's getting close to 0, regardless of its sign.

What you are saying would make perfect sense if you replaced "rate of change" with "the absolute value of the rate of change".

If we go back to the original question though:

Quote: Which of the following statement is true regarding the per capity cigarette consumption in the U.S. from 1960-2001?
...
iii. it is decreasing at an increasing rate
...

You could read the answers as "iii. its value is decreasing and the value of its rate of change is increasing" or "iii. its value is decreasing and it has a rate of change that is causing it to decrease at an ever-increasing rate", which shows the two interpretations we're arguing over.

I'd go with the physics perspective that the first half of the statement specifies a direction, implying the second half of the statement determines the magnitude in the already specified direction.

Quote: Original post by nilkn
I would have demanded clarification if I had encountered that on a test.

Really, this is the best thing to do. Well, aside from the demanding. Don't be an ass about it. I'd recommend asking for clarification instead.

The answers are ambiguous since it's not clear what convention is used. Three conventions are:
1) f is increasing if f' > 0 (increasing means more positive)
2) f is increasing if f*f' > 0 (increasing means moving further from zero)
3) f is increasing if f' > 0 while f' is increasing if f'*f" > 0 (looser, maybe what you'd use in everyday speech, "rate of change of the rate of change" is treated differently from the "rate of change")

As it stands:
(ii) is correct if we use convention (1)
(iii) is correct if we use convention (2) or (3)

If we shift the whole curve below the x-axis, then:
(i) is correct if we use convention (2)
(ii) is correct if we use convention (1)
(iii) is correct if we use convention (3)

The third, mixed, convention seems to be assumed in the OP:
(1) "Rate of change only includes a sign to show direction"
(2) "if a rate of change is decreasing, then it's getting close to 0, regardless of its sign"

This is actually a fairly common problem since you'll see all three and this is hardly the only area where competing conventions are used. I'd probably say the instructor should've given you the points, but that depends on the course and how and whether the convention was used in the course.


Lessons to be learned from this:
1) The wording used in the answers is ambiguous. (Learning to recognize ambiguities is very useful not only because there will be ambiguities but also because it leads to a better understanding of the domain.)

2) If an ambiguity affects the problem at hand, you should ask for clarification. (Don't be afraid to ask questions.)

3) If other students have received points after talking with this instructor about their exam and you would like to get points back in the future, then you should reevaluate how you approached him. Otherwise, just learn that this instructor doesn't negotiate with some group of people (whether "anyone" or "students" or whatever) that includes you.

[Edited by - Way Walker on May 27, 2010 12:33:52 AM]

Quote: Original post by nullsquared
What do you guys think?
(Sorry for posting here, but I don't really have anyone else to ask when I'm disagreeing with my math teacher)

I think that the summary graph (curve) tobacco+marijuana will be wuch interesting :))


[Edited by - Krokhin on May 28, 2010 11:44:36 AM]

Wow. That's just stupid by your teacher, IMHO. I mean, when you jump from a skyscraper, the falling speed doesn't decrease over time, or am I mistaken?

After a big discussion with the director of math and my teacher, the issue has been resolved. (Apparently there were also discussions with my teacher and the other math teachers.)

Resolved in the sense that you got points back, or, say, in that they decided to sentence you to death? You didn't really say.

Quote: Original post by Konfusius
Wow. That's just stupid by your teacher, IMHO. I mean, when you jump from a skyscraper, the falling speed doesn't decrease over time, or am I mistaken?

I do know that at some point the velocity of a falling body through air will no longer accelerate. Of course, as you fall, the amount of air increases so maybe this could cause your velocity to decrease. I can't remember if that actually happens though.

Quote: Original post by nobodynews

Quote: Original post by Konfusius
Wow. That's just stupid by your teacher, IMHO. I mean, when you jump from a skyscraper, the falling speed doesn't decrease over time, or am I mistaken?

I do know that at some point the velocity of a falling body through air will no longer accelerate. Of course, as you fall, the amount of air increases so maybe this could cause your velocity to decrease. I can't remember if that actually happens though.

Obligatory xkcd.