Understanding the Graph of an Equation | Calculus Help

[Bandarigoda]

Hi everyone, I'm learning calculus at school. Recently I was taught this equation like. Y = (2X^2)/(9 - X^2)
So the teacher did all by himself. So I came home and now confused. I know there are 3 graphs(sorry if the word is not right ) so I was doing it again. And I'm stuck at where to get the position of curves.

I got,
X = 0 , X = -3, X= 3
They are 3 graph. So I couldn't figure out how to get more positions and draw it. Unfortunately I can't remember what teacher did 100% .
So someone please demonstrate it for me from the steps I have done.

Thanks

 

[Bandarigoda]

I derived the functions and got their maximum /minimum

 

[Bandarigoda]

Here

 

[Mark44]

Hi everyone, I'm learning calculus at school. Recently I was taught this equation like. Y = (2X^2)/(9 - X^2)
So the teacher did all by himself. So I came home and now confused. I know there are 3 graphs(sorry if the word is not right ) so I was doing it again. And I'm stuck at where to get the position of curves.

I got,
X = 0 , X = -3, X= 3
They are 3 graph. So I couldn't figure out how to get more positions and draw it. Unfortunately I can't remember what teacher did 100% .
So someone please demonstrate it for me from the steps I have done.

Thanks

Your work for the derivative is correct: dy/dx = 36x/(9 - x²)²

I derived the functions and got their maximum /minimum

No, you differentiated the function and found the values for which f' = 0 or where the derivative is not defined.

If you set dy/dx = 0, the only solution is x = 0. The tangent line is horizontal when x = 0 (at the point (0, 0)).

dy/dx is undefined where the denominator is zero; namely, when x = 3 or x = -3. The original function is also undefined at the numbers. These turn out to be vertical asymptotes. The graph of the function tends to +∞ or -∞ on either side of these asymptotes.

Since there are two of them, they divide the number line into three intervals: (-∞, -3), (-3, 3), and (3, ∞). These intervals correspond to the three graphs you're talking about.

 

[Bandarigoda]

Hi, thank you very much Sir!