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

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

...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..

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,979

hi n1corponic

I'm on the case.  Stay on-line.

Welcome!

Bob

Children are not defined by school ...........The Fonz
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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hi;

Did you look at a graph at all?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,979

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

Children are not defined by school ...........The Fonz
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

bobbym wrote:

Hi;

Did you look at a graph at all?

Hi bobbym! 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: 7,979

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

Bob

Children are not defined by school ...........The Fonz
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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

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

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: 7,979

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

Children are not defined by school ...........The Fonz
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

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! 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: 7,979

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

Bob

Children are not defined by school ...........The Fonz
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

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.

Bob

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

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,979

hi n1corponic

You are welcome.  Post again if you need to.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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