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Math Help - Prove that maximum of sin^2(x)+sin^2(y)+sin^2(z) with x+y+z=180 is when x=y=z=60

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    Prove that maximum of sin^2(x)+sin^2(y)+sin^2(z) with x+y+z=180 is when x=y=z=60

    Prove that maximum of sin^2(x)+sin^2(y)+sin^2(z) with x+y+z=180 is when x=y=z=60
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    Senior Member MacstersUndead's Avatar
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    Quote Originally Posted by oleholeh View Post
    Prove that maximum of sin^2(x)+sin^2(y)+sin^2(z) with x+y+z=180 is when x=y=z=60
    This is a function from R^3 -> R. Find the Jacobian, (a 1x3 matrix, gradient). See if (x,y,z) = (60,60,60) is a critical point. then find the Hessian (the matrix of second order partial derivatives.), then use the second partial derivative test.
    Last edited by MacstersUndead; August 25th 2010 at 08:31 PM.
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