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Curve sketching Madness

  1. Feb 4, 2010 #1
    1. The problem statement, all variables and given/known data

    I need to sketch these curves and find where they intersect:

    x+y-y^3 = 0

    2. Relevant equations

    3. The attempt at a solution

    I have no idea what these are supposed to look like.. other than that x = -y^2+y is a sort of parabola that opens to the right.

    Any tips as to how to understand functions in these forms?
  2. jcsd
  3. Feb 4, 2010 #2
    These are easy, because you can get them in the form x=f(y). Just compute x for different values of y.
  4. Feb 4, 2010 #3
    Any general rule about how these look like without plotting the points?
    (Like for the thing with y^3?)
  5. Feb 5, 2010 #4


    Staff: Mentor

    The first equation can be written as x = y3 - y, and the second as x = y2 - y. At a point of intersection point, the x-value on one curve has to equal the x-value on the other curve, and the same is true for the y-values.

    Setting the two expressions for x equal gives us
    y3 - y = y2 - y
    This is simple to solve, and you don't need to plot any points to do it.
  6. Feb 5, 2010 #5

    Char. Limit

    User Avatar
    Gold Member

    He says he needs to sketch the curve as well, though.

    Quit thinking that the y-axis must be dependant. Pick some y points and find where the x values are at those points. You'll figure out the shape.
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