Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#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

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,394

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,394

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

Offline

#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.

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,394

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

Re: Can somebody please help me understand...


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#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)

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,394

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

Offline

#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?

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,394

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

Offline

#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!

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,394

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

Offline

Board footer

Powered by FluxBB