True/False on math tests. I think I am right, should I confront professor?

[1MileCrash]

In calculus III, I recently took an exam.

At the end of the test was a True/False question. I never know when to stop analyzing it.

Because of my apprehension, I went to her office after the test and she told me that the answer was true; I marked false. I had nothing to go off of at the time, and tried to remember the question and where I could have erred, and I accepted that I probably just messed up somewhere. She also said that the question was simple and not intended to be a trick, and that almost everyone correctly marked true.

Well we got the test back today, and I still think I am right, but only if you look at the problem really closely..

http://img535.imageshack.us/img535/7695/calciiitf.png

They way I see it, one of three possibilities could have gone down:

1.) The student writes the formula down for the directional derivative, barely pays attention to the diagram, sees that the formula is correct, and marks true.

2.) The student writes the formula down for the directional derivative, realizes that theta must be the angle between the gradient and the vector, notes that the vector in the diagram is not defined as the gradient, but then sees the perpendicular contours and realizes that it MUST be the gradient, and marks true.

3.) 1MileCrash realizes that although the contours are perpendicular to a vector, they are perpendicular to the wrong one, the unit vector u. Because of this, u is in the direction of the gradient, and the directional derivative is just ||grad f || since that theta is clearly not 0. 1MileCrash hesitantly marks false, wondering if he's overthought the problem.




Did I overthink the problem? What should I do? In my eyes, vector v here means absolutely nothing, so theta means absolutely nothing.

 

[micromass]

It's an awful picture. I've spent 15 minutes trying to interpret it, but no luck.
First of all, u in the picture is not a unit vector since it leaves in P.
Secondly, there is no chance at all that v would be the gradient. The gradient should actually point downwards since that's where the rate of change is highest. I have no idea what v is doing there.
Vector u seems to be perpendicular to the level curves and is in the direction of the greatest increase, so it's the gradient.

So (unless I'm an idiot and forgot most of my calc III), I think you have a point here. I would explain it to the professor.

 

[1MileCrash]

It's an awful picture. I've spent 15 minutes trying to interpret it, but no luck.
First of all, u in the picture is not a unit vector since it leaves in P.
Secondly, there is no chance at all that v would be the gradient. The gradient should actually point downwards since that's where the rate of change is highest. I have no idea what v is doing there.
Vector u seems to be perpendicular to the level curves, but that doesn't mean it's in the direction of the gradient. u seems to be opposite to the gradient.

So (unless I'm an idiot and forgot most of my calc III), I think you have a point here. I would explain it to the professor.

The gradient points up; the gradient always points towards the max rate of increasing change, and the values for f are increasing in the exact direction of u.

One way or another, it can't be true.

 

[micromass]

The gradient points up; the gradient always points towards the max rate of increasing change, and the values for f are increasing in the exact direction of u.

Yes, yes, I know. I already edited my post I'm stupid

 

[1MileCrash]

Yes, yes, I know. I already edited my post I'm stupid

Hah! Yeah, right.

 

[psparky]

If you think you are right...always discuss with your professor. You will end up getting to the bottom of it even if you are wrong.

Always stick up for yourself and what you believe. But if you are going to make an argument, make sure you have a sound reasoning for your disagreement. Because you will need to PROVE your point. But ya...professors are human just like you.

 

[nonequilibrium]

Yeah the professor mixed up the U and the V. I say you're totally correct. Weird that you're the only student with this problem?... If I were you I'd definitely go to the professor, but first ask your fellow students; it seems highly unlikely you're the only one with this problem, and if you got more students behind you, that's more convincing.

 

[FactorsOf2]

Definitely go talk with your professor, but go with an open mind (it will help you keep the right tone and avoid an attitude that will put her on the defensive).

 

[1MileCrash]

I showed her my reasoning and she said "looks like you may be right" but had to go to a meeting. In class, she asked who marked false on the test, (most people couldn't remember), said it should have been false, and to bring the test tomorrow if you marked false to get credit.

She added "thank jonathan for that." I'm just glad she didn't decide to take points away from those who marked true, then said my name!

So I'd say it went well, but I hope this doesn't negatively effect her opinion of me.

 

[micromass]

So I'd say it went well, but I hope this doesn't negatively effect her opinion of me.

On the contrary! I think you made a good impression on her as somebody who understands the material and pays attention to the details.

Congratulations that it went so well.

 

[mathwonk]

Good job! You were not only right, you stood up for yourself, made your point, AND won over the prof!

trifecta. superb. (and helped others.)

 

[DrummingAtom]

I'm just glad she didn't decide to take points away from those who marked true, then said my name!

LOL. That would be rough.

 

[20Tauri]

Well done! I wouldn't worry about her being angry--the professors at my school always like it when we find and point out mistakes, because it means we're paying attention.