Can somebody please help me understand...

n1corponic · 2012-09-25 05:17:42

...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..

Bob · 2012-09-25 05:35:32

hi n1corponic

I'm on the case. Stay on-line.

Welcome!

Bob

bobbym · 2012-09-25 05:37:52

Hi;

Did you look at a graph at all?

Bob · 2012-09-25 05:44:22

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

n1corponic · 2012-09-25 05:45:12

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.

Bob · 2012-09-25 05:49:05

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

Bob

bobbym · 2012-09-25 05:54:30

Hi;

This might help too.

http://ltcconline.net/greenl/courses/11 … crease.htm

n1corponic · 2012-09-25 05:56:59

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)

Bob · 2012-09-25 06:03:33

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

n1corponic · 2012-09-25 06:13:35

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?

Bob · 2012-09-25 06:25:55

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

n1corponic · 2012-09-25 06:33:06

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!

Bob · 2012-09-25 06:42:31

hi n1corponic

You are welcome. Post again if you need to.

Bob

Math Is Fun Forum

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

Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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

Re: Can somebody please help me understand...

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