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Homework Help: Graph of an equation

  1. Jun 13, 2013 #1
    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.

  2. jcsd
  3. Jun 13, 2013 #2
    I derived the functions and got their maximum /minimum
  4. Jun 13, 2013 #3
  5. Jun 13, 2013 #4


    Staff: Mentor

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

    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.
  6. Jun 18, 2013 #5
    Hi, thank you very much Sir!
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