Function monotony for f' not equal to 0

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nisakos

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I need help with a function's monotony.
I try to find first derivative and its roots but..
My first derivative is 1/x^2 so there is no roots.
What i have to write about monotony and min or max of function.

2) if derivative has a root x=-2 but -2 is not in the domain of function what a gave t say about monotony?

3) if the second derivative is something like 1/x^2 what about tha curve of function?

Please help me , i am a student and i trying to understand something more special subjects for my exams.

Thanks
 
nisakos said:
My first derivative is 1/x^2 so there is no roots.
What i have to write about monotony and min or max of function.
2) if derivative has a root x=-2 but -2 is not in the domain of function what a gave t say about monotony?
3) if the second derivative is something like 1/x^2 what about tha curve of function?
Click to expand...
This posting is an absolutely perfect example of how not to ask a question here.
From this, we have no idea what the original problem is, much less what the poster does no understand.

@nisakos, if you want help: post the entire original question. Do not drop us into the middle of something you have done expecting us to follow you.
 
Ok i want to find the monotony of function
f(x) = (-x-2)/ x

I alreadg calculate f'(x)= 2/ x^2
And there are not roots for the equation f'=0
So which is the answer about mononoty of f ?
Moreover f" = 4/ x^3 so again no roots.what about the curve? ( i dont known the word in english)

My other question is for function sqrt(x) / (2-x).
f'(x) = (2+x) / ( 2 sqrt(x) (2-x)^2 )

Roots? What about monotony


Thanks again and i am not an english speaker so sorry for my english
 
nisakos said:
Ok i want to find the monotony of function
f(x) = (-x-2)/ x
Click to expand...
Much better, thank you.
See the graph HERE.
Now note that you have a sign error in the second derivative: y''={-4}/{x^3}.
 
Ok great i know it. My question is generally if i have a function like that and and i dont know the graph what i am going to do.
 
nisakos said:
Ok great i know it. My question is generally if i have a function like that and and i dont know the graph what i am going to do.
Click to expand...
You seem to be is real need of a live tutor.
 
Okay, so the original equation you started with was \(\displaystyle f(x)=\dfrac{-x-2}{x}\), and you need to prove that it's monotonous. Just looking at its graph, we can see that the function is always increasing on the intervals \(\displaystyle (-\infty, 0)\) and \(\displaystyle (0,\infty)\). So now let's prove that. You've correctly identified the first derivative as \(\displaystyle f'(x)=\dfrac{2}{x^2}\) and you're also correct in noting that there are no roots of the first derivative. So, what does that tell you? Does the first derivative ever change sign? If so, where? If it doesn't, do you know why it doesn't change? What can you infer from all of this information? How does all of this help you solve the problem?

If you need a refresher on these type of problems, you might try herehttp://sites.csn.edu/ehutchinson/notes/4_3notes181.pdf.
 
Great really really thank you.

It is easy for you to tell me something about also for f" and what about curvature if there is no roots? Because increasing or not i checked from the graph but the curvature ?
 
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