i'm trying to strenthen my graph skill

[logistic_guy]

here is the question

Find the extrema of the function $\displaystyle f(x) = \frac{x+1}{\ln(1-2x)}$.

my goal to this question isn't only to solve and get solution. i want to understand how to understand the graph of any function. i read on internet if i find the extrema of function i can understand the behavior of the function which help me approximate its graph. i discover if i know visualise graph i can solve the question quickly in my last 20 questions i solved. graphs or algebra in general is my weaknes and i'm working hard to understand.

where do i start? take derivative? or find domain? my think tell me of previous questions denomintor can't be zero this mean $\displaystyle \ln(1 - 2x)$ can't zero. is my think correct so far?

 

[blamocur]

i want to understand how to understand the graph of any function.

Good luck with that
Finding the domain is, IMHO, a good first step.
I also often find it useful to draw a graph on my computer. There are lots of different packages, and most of them require time to learn. Personally, I usually use Numpy and Matplotlib, but I am a software engineer. There might be easier online tools, but I'll leave it to more knowledgeable members to comment.
In your particular example you want to take into account the fact that logarithms have limited domain in real numbers.

 

[logistic_guy]

thank blamocur

you advice me first step to download a software that graph functions? but this will let cheat how this graph go. my goal is to understand graph without looking. is this imppossible? i deal with log before but i never solve for zero

$\displaystyle \ln(1 - 2x) = 0$ i don't know to solve this. do you mean log is limited domain and i don't need to solve for zero? i don't understand

my first thing is to do this

$\displaystyle \ln(1 - 2x)^2 = 0^2$

$\displaystyle 1 - 2x = 0$

$\displaystyle - 2x = 1$

$\displaystyle -x = \frac{1}{2}$

 

[blamocur]

ln(1−2x)=0 i don't know to solve this.

I remember you being told (I believe by @BigBeachBanana) in a different thread that you really need to work on some elementary stuff before trying to understand more advanced things. I support that advice wholeheartedly.

As for the graphs, I am not sure what your actual goal is. If you feel that using software is cheating then pick several values of 'x', compute the corresponding values of f(x) and plot the points on a piece of paper. That's how I did it before computers became widely available. If you can find roots of the function that might help too. Computing derivatives and finding their roots to get a sense of min/max values might be more difficult but still doable in some cases.
Did you try to search the net. A quick query "how to graph a function" produced a list which might be useful.

 

[Otis]

i read on internet if i find the extrema of function i can understand the behavior of the function

Do you believe that?

Here are the extrema of a function:

Global maximum: None
(y approaches +∞ as x approaches 0 from the left)

Global minimum: None
(y approaches -∞ as x approaches -∞ or 0 from the right)

Local maximum: (1/2, 0)

I'm wondering whether you think this is enough information to claim that you understand the function's behavior. What happens, if you try to draw the graph?
$\;$

 

[Otis]

work on some elementary stuff before trying to understand more advanced things.

I don't think logistic_guy has any interest in doing that.
$\;$

 

[blamocur]

I don't think logistic_guy has any interest in doing that.
$\;$

Maybe. But he seems eager to learn, and I felt he isn't going to advance without a solid base.

 

[Otis]

he isn't going to advance without a solid base.

Oh, I completely agree with you and BigBeachBanana. I just don't see it happening.

 

[Otis]

$\displaystyle \ln(1 - 2x) = 0$
$\displaystyle -x = \frac{1}{2}$

A serious student checks their results.
$\;$

 

[blamocur]

A serious student checks their results.
$\;$

Good catch. I didn't notice this

 

[logistic_guy]

I remember you being told (I believe by @BigBeachBanana) in a different thread that you really need to work on some elementary stuff before trying to understand more advanced things. I support that advice wholeheartedly.

As for the graphs, I am not sure what your actual goal is. If you feel that using software is cheating then pick several values of 'x', compute the corresponding values of f(x) and plot the points on a piece of paper. That's how I did it before computers became widely available. If you can find roots of the function that might help too. Computing derivatives and finding their roots to get a sense of min/max values might be more difficult but still doable in some cases.
Did you try to search the net. A quick query "how to graph a function" produced a list which might be useful.

not only BigBeachBanana but everyone is telling me that. i'm not against that. i just don't know how to improve. i'm read pages and solve everyday with no effect

i try to graph by points before i fail to graph correct

Do you believe that?

Here are the extrema of a function:

Global maximum: None
(y approaches +∞ as x approaches 0 from the left)

Global minimum: None
(y approaches -∞ as x approaches -∞ or 0 from the right)

Local maximum: (1/2, 0)

I'm wondering whether you think this is enough information to claim that you understand the function's behavior. What happens, if you try to draw the graph?
$\;$

i'm understand why you confuse. i mean by extrema

1. max min
2. concav up down
3. increase decreas
4. horizont vertic asympto
5. critic points

it's true extrma mean max and min but back in Calculus 1 when the question say find extrema we find this 5 thing

I don't think logistic_guy has any interest in doing that.
$\;$

why you say this

A serious student checks their results.
$\;$

i'm not understand why you think i don't check? i'm study curves now and i know the graph of square root and log almost same

$\displaystyle \sqrt{1 - 2x}$
$\displaystyle \ln(1 - 2x)$

i think it's only the log is shifted to the right little

this operation work in square root

$\displaystyle \sqrt{1 - 2x}^2 = 0^2$

$\displaystyle 1 - 2x = 0$

$\displaystyle -2x = 1$

$\displaystyle -x = \frac{1}{2}$

i think we can do the same to log because they almost have the same graph

 

[blamocur]

If -x = 1/2 then what is the value of 1-2x. You really should be able to figure out and double check the stuff like this.

not only BigBeachBanana but everyone is telling me that. i'm not against that. i just don't know how to improve. i'm read pages and solve everyday with no effect

Different courses in colleges have different prerequisites. It makes no sense to try learning, say, differential geometry or even introductory calculus without mastering elementary algebra. You'll be wasting your time and self-esteem without much progress.

 

[mario99]

here is the question

Find the extrema of the function $\displaystyle f(x) = \frac{x+1}{\ln(1-2x)}$.

where do i start? take derivative? or find domain?

Take the derivative.

I don't know if you know the quotient rule, but I am 100% sure that you are an expert in the product rule. Therefore, write the function as:

$\displaystyle f(x) = (x+1)\ln(1-2x)^{-1}$

It's your game now to apply the product rule. (Just remember the two objects.)

 

[Otis]

the graph of square root and log almost same

Here are two views of those graphs.


$\;$

 

[Otis]

i'm not understand why you think i don't check?

The reason why is because you keep posting obvious, beginning algebra mistakes in your threads. Your value for x does not work.
$\;$

 

[Otis]

i mean by extrema

1. max min
2. concav up down
3. increase decreas
4. horizont vertic asympto
5. critic points

That is close to being 20% correct, but not quite.
$\;$

 

[Otis]

I am 100% sure that you are an expert in the product rule … Just remember the two objects.

$\;$

 

[mario99]

Don't worry about it Mr.Otis. The OP knows what I mean.

 

[logistic_guy]

today i felt like i'm mastering algebra. i come back to this question and i'm shocked i still can't solve it

why?

what should i do?