Mathematics - 2012-04-06 (page 4 of 4)

Jordan

22:13

I just found out that I have to get all As for the next year to be able to meet the minimum GPA requirement

is that even possible? are there people that do that

robjohn

@KannappanSampath http://chat.stackexchange.com/transcript/36/2012/4/5

Oh, I see tb already got it.

Kannappan Sampath

I am still unable to see what Matt referred to.

@robjohn Thank you, any way. :)

t.b.

Am I being obtuse?

Jonas Teuwen

@MattN Wait. What?

Kannappan Sampath

Oh, I see. Let me read through and get back.

robjohn

22:20

@tb I can't make sense of it right off.

t.b.

Will will love those last few pages of the transcript :)

^ another one for him :)

robjohn

:-)

@JonasTeuwen no you didn't really :-)

@tb the deletions won't show in the transcript.

t.b.

they will if he uses the "load to my last message" feature.

Kannappan Sampath

Me neither.

robjohn

@MattN did I abuse tb and not remember? darn!

Kannappan Sampath

22:24

I never saw that...

Chrome snapped.

The "I never saw that" was referring to Rob's message flash.

Sorry no offense intended for anyone.

Jonas Teuwen

I feel very offended.

robjohn

@JonasTeuwen by?

Jonas Teuwen

I don't know 8-).

t.b.

@robjohn Kannappan, who else? He's always offending me... :)

robjohn

@JonasTeuwen So you're offended by ignorance?

Jordan

22:29

If I am trying to optimize something and I am trying to find the derivative of something like (4x+2)^2 = area can I just find the derivative of 4x+2 and then square the resulting area?

Jonas Teuwen

Yes! 8-).

Kannappan Sampath

@tb Hmmm, Really?

robjohn

@Jordan perhaps I am not understanding your question

Jordan

Oh why not?

t.b.

@KannappanSampath oh, boy... No, don't worry; it was just a silly joke on your being afraid of offending somebody where there is not the slightest chance of any kind of offense in your four posts. :)

robjohn

22:32

In the case of $(4x+2)^2$, you can

Jordan

I am trying to find the derivative of (4x+2)^2 = area, to simplify finding the derivative can I say that the derivatives squar rootis equal to that results square

Kannappan Sampath

@tb :)

robjohn

However in general, say $1+(4x+2)^2$ this doesn't work

Actually, let's go back to your example..

$\text{area}=(4x+2)^2$

take the derivative of $4x+2 \to 4$

that never equals $0$

Jordan

I don't know what that means...4?

robjohn

You asked about taking the derivative of $4x+2$. That is $4$

Jordan

22:38

yes

but when trying to optimize the area of something is it okay to factor things out of the formula and then apply those later after you derive?

robjohn

@Jordan you have to be careful that everything is monotonic

Jordan

I do not know what monotonic is

robjohn

so what you want to do is to optimize the square root and then square that to get the final answer?

Jordan

yes

t.b.

@robjohn I think the question really is not about slick tricks but rather on how to compute the derivative of a polynomial.

For those the answer is simply: no you're not allowed to simplify this way.

Jordan

22:43

I am just looking for an easier way to do some optimization problems

I dont understnad if I have $(4x^2 + 3x +2)/2 = area$ why cant I just have $(4x^2 + 3x +2) = 2area$

t.b.

This is perfectly fine.

What makes you think that this wouldn't be okay?

Jordan

I am trying to do it now and it doesnt really seem to work

t.b.

So you want to find the $x$ such that the area is minimal, right?

Jordan

yes

t.b.

So, what did you get?

Kannappan Sampath

22:48

Got it I believe!

OK!

t.b.

The first step would be to take the derivative of the left hand side.

What did you get for that?

Jordan

well for something simple if I have something like $(3x+2)^2$ the derivative would be $6(3x+2)$

robjohn

@Jordan yes.

t.b.

right. But you had $(4x^2 + 3x + 2)$ before.

Jordan

so for x=2 I would get 48, but if I were to take the square of (3x+2) it wouldn't be the same

t.b.

22:50

Why $x = 2$?

Jordan

just a random number

robjohn

@tb okay, I am totally missing his point then :-)

sorry, I had to go afk for a while

t.b.

@Jordan okay. But the question was to find the minimal area, so you now have to find the roots of the derivative.

Jordan

Oh...so the values won't be the same...but the roots will?

t.b.

Wait. You have $\text{area} = (3x+2)^2$ in your latest example. Now you want to find the $x$ for which this is minimal.

Jordan

22:53

well actually now I am confused because the roots are $-2/3$ and then for the other one it is the square root of -2/3

t.b.

You computed the derivative correctly to be $6(3x+2)$.

And the root is $-2/3$.

robjohn

@tb sorry, I was thinking too generally.

@Jordan: this is the case that I was talking about earlier, where the roots of the derivative are the same as the roots of the function.

Jordan

Ok and then to find the square root of the derivative of 3x+2

but you cant find the square root of a negative

robjohn

no find the roots... that is where $6(3x+2)=0$

not the square roots

Jordan

find the roots and them find the square roots of those?

that is -2/3s for both

robjohn

22:58

why are you taking square roots?

Jordan

instead of finding $(3x+2)^2$ can't I find the square root of the derivative of $(3x+2)$

robjohn

no. what you want to do is to take the derivative of the area, find where it is 0 and plug that back into the area

If the values of where the derivative is 0 make sense.

In your example, the derivative of the area is $6(3x+2)$

Kannappan Sampath

@Jordan Your comments under Arturo's answer are rather rude.

Jordan

which ones?

Kannappan Sampath

Please delete them and respect the suggestions you have been given.

Jordan

23:03

I don't see how it is disrespectful to disagree with someone, that is what I believe because it is what I see to be true with empirical evidence.

Kannappan Sampath

If confusion persists about Rolle and MVT, you can ask for clarifications. But, choosing to disagree there seems to me, not a wise thign to do.

Jordan

Ok so it is always wrong to say that the derivative of $(3x+2)^2 = x is the same as (3x+2) = \sqrt{x}$

Oh well I do not understand what he is trying to say because my book says something else

Kannappan Sampath

I recall Prof. Jyrki here. I was foolish. Thanks to @tb for saving me from further shame.

@Jordan So, why do you hold him at fault? It is YOU who did not understand. Not they, Right?

Jordan

I do not hold him at fault, I am just trying to learn

Kannappan Sampath

But, that is not evident from your comments there.

robjohn

23:07

@Jordan it is alway wrong to say the derivative of $(3x+2)^2=x$

Jordan

ok...

so instead of x on the left make it 2

robjohn

you can take the derivative of a function, not an equation (but you can take the derivative of both sides of an equation)

t.b.

I hate it when this happens :)

b/c there's the $L^2$-SP?

IOW what's an i.p.s?

Kannappan Sampath

Indian Police Service?

It's plain silly?

Hmm. I give up. I cannot think of mathematical ips-es.

robjohn

@tb shouldn't that either be $C[0,2\pi]$ or $e^{i2\pi nx}$?

Jordan

23:13

Okay then so if I am trying to find the optimization of something then what do I do if the formula is too complex to derive?

Kannappan Sampath

@Jordan There never is. :)

@tb But, why after this long?

It's old--very old.

Jordan

Okay then so if I am trying to find the optimization of something then what do I do if the formula is too complex for me to derive?

t.b.

@robjohn yes, of course. I'm still dumbfounded by the i.p.s.

@KannappanSampath for some reason Matt bumped the question.

Kannappan Sampath

@tb Hah. Did not notice. Thank you.

robjohn

@tb The Inner Product Space comment disappeared.

@tb but Sam's comment seems to address most points.

Jordan

23:18

I just spent an hour trying to learn about MVT and learned nothing

Kannappan Sampath

It might be a feeling.

Given you had the guts to say Arturo was confusing between things. :P

Well, time to hit the bed. Bye. (for real, @tb)

Jordan

23:38

so an inverse trig function is the inverse of the result of the function correct?

t.b.

@MarianoSuárezAlvarez: I tried to support your comment, but so far with little success :/

Jordan

It is so depressing to be failing high school math in my mid twenties, that dude on here is 17

t.b.

May I ask for a few votes on this comment so that it becomes visible "above the fold"?

Mariano Suárez-Alvarez

Jordan, please try to limit the drama

Jordan

23:58

how do I find roots for (x^2-x)=16?

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$Mathematics$ Mathematics