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MAX/MINS with multivariables

  1. Oct 3, 2005 #1
    Hey I was wondering if anyone can tell me if i am doing this right.

    f(x,y) = xy^2 ; R is the circular disk x^2+y^2<=3

    So first i took the gradient, since I know a mix/min can exist if the gradient is equal to 0.

    Gradient of X= y^s
    Gradient of Y= 2xy

    So the point (0,0) can be considered right?

    Anyway, I know I have to test region edges, so I parameterized the equation.

    r(t) = <radical 3 cos(t),radical 3 sin(t)>

    i plugged those values of x and y into my equation , and then took the derivative.

    After some simplification, I came up with

    sin(t)(3*radical3*cos(t)^2-3*radical3)

    t= 0, pi, pi/2, 3pi/2 (right?)

    so i found the x and y value when t is equal to those values

    in conclusion, i have these points.

    (0,0)
    (0,radical3)
    (0,-radical3)
    (radical3,0)
    (-radical3,0)

    I tested these values in the equation xy^2 = f(x,y)

    and found that there is no max or min....i dont think this is right.

    Can someone help me find my mistake?
     
  2. jcsd
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