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Multivariable Calc Absolute Extrema Problem

  1. Mar 29, 2010 #1
    1. The problem statement, all variables and given/known data
    F(x,y)= sin(x)sin(y)sin(x+y) over the square 0[tex]\underline{}<[/tex]x[tex]\underline{}<[/tex]pi and 0[tex]\underline{}<[/tex]y[tex]\underline{}<[/tex]pi

    (The values for x and y should be from 0 to pi INCLUSIVE)

    2. Relevant equations

    3. The attempt at a solution

    I know I need to do the partial derivatives in terms of x and y and set them equal to 0 to find the critical points, but I am having some trouble with that.
  2. jcsd
  3. Mar 29, 2010 #2
    Do you know [itex]\frac{\partial}{\partial x}\sin(x)[/itex], [itex]\frac{\partial}{\partial x}\sin(y)[/itex] and [itex]\frac{\partial}{\partial x}\sin(x+y)[/itex]? You can use the product rule to put them together- it works the same with partial derivatives. Then do the same but with [itex]\frac{\partial}{\partial y}[/itex].
  4. Mar 29, 2010 #3

    I already found that:

    partial derivative in terms of x = siny[cosxsin(x+y)+sinxcos(x+y)]
    you get y=0, pi because siny =0, but I don't know how to solve for the other solutions

    partial derivative in terms of y = sinx[cosysin(x+y)+ sinycos(x+y)]
    and you get x=0, pi because sinx=0

    and then I have the same problem again and am stuck
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