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#1 2012-11-08 08:44:00

Karimazer1
Guest

Differentiation interpretation help!

Hey! It's been a while! Hope you are all good!

I have simple thing I cannot get my head around.

So far; the function that we want to maximise is x1^2/2 +x1x2.

Differentiated, gives x1+x2.

SOC is x2.

1. General question - if the SOC = 0...what does that mean? I.E When SOC<0 =max, SOC>0 =min, what do you say when SOC=0?

2. x1 AND x2 can be -1, 0 or 1. We want to find the maximum. Is the following correct?

IF x2 = 1, x1 will be maximised when x1=1, but SOC is 1 (>0) therefore, this is a minimum...so it is not a maximum?

IF x2 = -1, x1 will be maximised when x1=1 too, now SOC is -1 <0 therefore maximum!

Please help me answer the first general question and let me know if my working/logic behind the second question is correct ! Thank you !!!!

#2 2012-11-08 09:03:15

bobbym

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Re: Differentiation interpretation help!

Hi;

Welcome back!

SOC?

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2012-11-08 09:13:52

Karimazer1
Guest

Re: Differentiation interpretation help!

Second order condition, sorry.

I don't know what is wrong with me, it seems my basic basic maths skills have gone. I've just...forgotten?

I mean (in addition to the above!) when you differentiate x1+x2 with respect to x1, you do get x2, right? And not 1+x2?
Same applies the other way, with x2-x1, differentiate with respect to 2, we get -x1 right? not 1-x1?

Thank you !!

#4 2012-11-08 09:58:09

bob bundy
Moderator

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Re: Differentiation interpretation help!

hi Karimazer1

Here's what I'm getting for your first question.

(i) You've differentiated to find stationary points.

(ii) you've differentiated a second time so you can say max or min.

But what to do if the second differential is zero?

Answer you cannot easily tell I'm afraid.

Consider these graphs all with d2y/dx^2 = 0

y = x^3   This has a point of inflexion at x = 0

y = x^4  This has a minimum at x = 0

y - -x^4 This has a maximum at x = 0

I seem to vaguely remember somebodies rule that you keep differentating until you don't get a zero but I'm uncertain. (have to do some research)

Now to the second question.

Are you treating x1 and x2 as independent variables and you are using partial differentiation ?

Because now we have other possibilities.  As well as max and min you can have saddle points (max in one plane but min in the other) or even max for one variable but no stationary point for the other variable.

Suggest you start by defining this more clearly.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#5 2012-11-08 10:28:23

anonimnystefy
Real Member

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Re: Differentiation interpretation help!

Hi

http://en.wikipedia.org/wiki/Higher-order_derivative_test

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#6 2012-11-08 23:53:03

Karimazer1
Guest

Re: Differentiation interpretation help!

Ok can we please start simply?

If:

x1/2 + x1x2

What is it differentiated?
Then what is that differentiated again?

It is; 1? Right?

Thanks

#7 2012-11-09 00:22:37

bob bundy
Moderator

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Re: Differentiation interpretation help!

hi Karimazer1

If

The deltas are used in place of 'd'  to show that one variable is being treated as a constant while differentiation is applied to the other.

On a 3D graph, the result is as if you had cut through the surface with a plane parallel to one of the x axes.

To come back to your question, which variable are you differentiating with respect to ?

Bob'

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#8 2012-11-09 04:22:29

Karimazer1
Guest

Re: Differentiation interpretation help!

Hi bob thank you. I mean

If y = (x1)/2 + x1*x2

So the SOC is still 1? Right? Or am I wrong?

#9 2012-11-09 04:23:27

Karimazer1
Guest

Re: Differentiation interpretation help!

Diferentiating with respect to x1,

there are two variables, x1 and x2

y = x1/2 +x1x2

first time = x1 + x2
second time is 1?

#10 2012-11-09 05:49:38

bob bundy
Moderator

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Re: Differentiation interpretation help!

hi

Looking back I see you had a different function

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#11 2012-11-10 01:21:09

Karimazer1
Guest

Re: Differentiation interpretation help!

Thank you Bob so much!