i'm trying to strenthen my graph skill

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logistic_guy

Junior Member
Joined
Apr 17, 2024
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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?
 
logistic_guy said:
i want to understand how to understand the graph of any function.
Click to expand...
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.
 
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

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

\(\displaystyle 1 - 2x = 0\)

\(\displaystyle - 2x = 1\)

\(\displaystyle -x = \frac{1}{2}\)
 
logistic_guy said:
ln(1−2x)=0 i don't know to solve this.
Click to expand...
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.
 
logistic_guy said:
i read on internet if i find the extrema of function i can understand the behavior of the function
Click to expand...
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?
[imath]\;[/imath]
 
blamocur said:
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.
Click to expand...
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

Otis said:
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?
[imath]\;[/imath]
Click to expand...
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

Otis said:
I don't think logistic_guy has any interest in doing that.
[imath]\;[/imath]
Click to expand...
why you say this :(

Otis said:
💡 A serious student checks their results.
[imath]\;[/imath]
Click to expand...
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
 
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.

logistic_guy said:
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
Click to expand...

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.
 
logistic_guy said:
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?
Click to expand...
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:

[imath]\displaystyle f(x) = (x+1)\ln(1-2x)^{-1}[/imath]

It's your game now to apply the product rule. (Just remember the two objects.) 😉
 
logistic_guy said:
i'm not understand why you think i don't check?
Click to expand...
The reason why is because you keep posting obvious, beginning algebra mistakes in your threads. Your value for x does not work.
[imath]\;[/imath]
 
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