How to Analyze the Function f(x)=2x/(x²-4) Using Calculus?

[Dre22]

1 domain & range
2 X & Y intercept
3 All Asymptotes
4 use the first derivative test find all critical values, intervals where the graph in increasing and or decreasing, and relative extrema.
5 use the second derivative test find all critical values, inflection points, and where the graph is concave up or down.


f(x)= 2x/x²-4

f¹(x)=-2(x²+4)/(x²-4)²

f²(x)=4x(x²+12)²/(x²-4)³
I have it most done. I want to see if I have it right. show work please to follow

 

[vociferous]

You can check your answers by graphing the equations with a computer or calculator.

 

[Dre22]

i know
i need to show work

 

[vociferous]

The first thing to do would be to see where the equations equal zero. The function zeros will give you your intercepts. The first derivative zeros will give you your local minima and maxima, and your second derivative zeros will give you your points of inflection. You need to make a table of the equation, and the first and second derivatives of the equation at all these critical points. Also, you should take the limit of the equation as it approaches positive and negative infinity. This will allow you to sketch the graph.

For calculus I, you should always sketch the graph before using a computer or graphing calculator to check your work.

 

[Borek]

I have it most done. I want to see if I have it right. show work please to follow

It doesn't work this way. It is you who wants to see if your work is OK, so you post what you did.

 

[Defennder]

I have it most done. I want to see if I have it right. show work please to follow

On the other hand, if you just want to check if you got the right answers and you're lazy to post your work here, just post your answers and we can verify it for you. But don't expect any explanation if you didn't show your work.

 

[Dre22]

my scanner is not working with my lap top.

 

[Borek]

Tex you go then.

You will learn a new skill.