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#1 2012-09-25 05:17:42

n1corponic
Member
Registered: 2012-09-10
Posts: 7

Can somebody please help me understand...

...how we find the interval where the function e^x-e^(3x) is increasing... the derivative is e^x[1 - 3e^(2x)]. I have the answer but I feel lost.. hmm

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#2 2012-09-25 05:35:32

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Can somebody please help me understand...

hi n1corponic

I'm on the case.  Stay on-line.

Welcome!

Bob


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

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#3 2012-09-25 05:37:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

Re: Can somebody please help me understand...

Hi;

Did you look at a graph at all?

View Image: 2012-09-25_103500.gif

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.

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#4 2012-09-25 05:44:22

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Can somebody please help me understand...

OK, here we go.

Your differentiation is correct.  For an increasing function you want dy/dx to be > 0

e^x is always positive so you need

log base e  is an increasing function so the inequality holds if you take logs

Graph below.

Bob

View Image: nicorponic.gif

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

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#5 2012-09-25 05:45:12

n1corponic
Member
Registered: 2012-09-10
Posts: 7

Re: Can somebody please help me understand...

bobbym wrote:

Hi;

Did you look at a graph at all?

Hi bobbym! smile I took a look at the graph in wolframalpha or smth..but it won't help on my future exams.. if i do not know how to find the answer on my own.

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#6 2012-09-25 05:49:05

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Can somebody please help me understand...

My post 4 may have been missed as bobbym and I posted together.

Bob


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

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#7 2012-09-25 05:54:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

Re: Can somebody please help me understand...


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.

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#8 2012-09-25 05:56:59

n1corponic
Member
Registered: 2012-09-10
Posts: 7

Re: Can somebody please help me understand...

bob bundy wrote:

OK, here we go.

Your differentiation is correct.  For an increasing function you want dy/dx to be > 0

e^x is always positive so you need

log base e  is an increasing function so the inequality holds if you take logs

Graph below.

Bob

Your approach seems wonderful!!! and according to me correct.. but why does the book i have give another..but very similar answer?.. it says x<or=-1/2*ln3  Is it the same but i'm missing smth??

Last edited by n1corponic (2012-09-25 05:59:02)

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#9 2012-09-25 06:03:33

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Can somebody please help me understand...

hi n1corponic

They are the same because

But the book shouldn't be saying less than and equal to because the graph has a turning point when = so dy/dx = 0

So the value of the function isn't getting bigger.

Bob


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

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#10 2012-09-25 06:13:35

n1corponic
Member
Registered: 2012-09-10
Posts: 7

Re: Can somebody please help me understand...

bob bundy wrote:

hi n1corponic

They are the same because

But the book shouldn't be saying less than and equal to because the graph has a turning point when = so dy/dx = 0

So the value of the function isn't getting bigger.

Bob

wow! they are the same indeed! big_smile I feel sooooo much better now!

Well, the book says (-infinity, -1/2*ln3] , so I guess it includes -1/2*ln3 probably because the question doesn't ask where the fuction strictly...increases..that must be it! right?

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#11 2012-09-25 06:25:55

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Can somebody please help me understand...

The square bracket means include the endpoint.  It seems I am assuming too much.  If it doesn't say strictly, I concede the argument.

smile

Bob


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

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#12 2012-09-25 06:33:06

n1corponic
Member
Registered: 2012-09-10
Posts: 7

Re: Can somebody please help me understand...

bob bundy wrote:

The square bracket means include the endpoint.  It seems I am assuming too much.  If it doesn't say strictly, I concede the argument.

smile

Bob

Thank you for everything!!!!!!! bob bundy!!!!!! plus congrats to owner..admins..moderators etc. for this great site! big_smile cheers!

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#13 2012-09-25 06:42:31

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Can somebody please help me understand...

hi n1corponic

You are welcome.  Post again if you need to.  smile

Bob


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

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