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Maximum and minimum values

  1. Feb 24, 2012 #1
    Find the maximum and minimum values of f(x,y) = x+2y on the disk
    x2+y^2 ≤1

    I have this for now:

    f_1(x,y) = 1
    f_2(x,y) = 2

    x=cos(t) and y=sin(t)

    I have that g(t) = x(t) + 2*y(t) --> g(t) = cost(t) + 2*sin(t)

    g'(t) = 0 = 2*cost-sin(t)

    Then I can see that:

    2cos(t)/cos(t) -sin(t)/cos(t) = 0/cos(t) --> tan = 2

    That is the parameterization, right?

    From this point I have no idea what to do.
    Last edited: Feb 24, 2012
  2. jcsd
  3. Feb 24, 2012 #2

    Ray Vickson

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    Homework Helper

    Find the value or values of t that give tan(t) = 2. Or, since you only need sin(t) and cos(t), why not express them in terms of tan(t)?

    Last edited: Feb 24, 2012
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