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Points where gradient is zero (plotting it)

  1. Apr 15, 2007 #1
    1. The problem statement, all variables and given/known data

    A curve has equation:


    Find the co-ordinates of the points on the curve where dy/dx=0

    I think I was able to differentiate it and get the coordinates fine, but I'm wanting to plot the function in Mathematica (5.2) to see if I'm right or not (BTW, I tried Ma's Dt[] and Differential[] functions, but I can't interpret the results. And plot[f, {x,-2,2}] just gives me error messages because y is undefined).

    2. The attempt at a solution





    For the fraction to equal zero, the numerator must also be zero, therefore:


    Given this, substituting this value for y:


    Therefore (using the quadratic formula):


    but it seems a little hackish to me, this from a past-paper (Edexcel Advanced Level C4, 28th June 2005), usually you get integer answers.

    But besides asking if I'm right, how can I plot functions with multiple instances of x and y within? I'm guessing I'd need to convert it to a parametric somehow.
  2. jcsd
  3. Apr 15, 2007 #2
    diff. gives [itex] \ 2x + 2x \frac{dy}{dx} + 2y - 3(2y \frac{dy}{dx} ) = 0 [/itex]
  4. Apr 15, 2007 #3
    Where did [itex]+2y[/itex] come from? I didn't have a solitary [itex]y^2[/itex] expression.

    EDIT: Ah I see, product rule; I forgot to reapply the coefficient (2) of xy after performing the product differentiation.

    Still, how can I plot the function?
    Last edited: Apr 15, 2007
  5. Apr 15, 2007 #4
    the question is asking for the critical points of the surface right? I have a question do you need to graph this function? Do you need to find the saddle points and min max?
  6. Apr 15, 2007 #5
    I'm not being asked to plot the graph, and I've since found what I think are the right co-ordinates (by substituting the resolved value of y into the equation and solving) as [itex]{ (2,0) , (-2,0) }[/itex].

    I want to plot the graph out of personal curiosity, to see what the graph actually looks like (but also to make sure I'm right). I haven't covered the plotting of implicit functions on my curriculum's syllabus though. Hence why I'm asking :)
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