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Math Help - A unique minimum for a 2 variables function?

  1. #1
    MHF Contributor arbolis's Avatar
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    A unique minimum for a 2 variables function?

    I must tell the veracity of the affirmation : f(x,y)=\sin (x) + \cos (y) +a(x+y) has a unique minimum if a>1.
    My attempt : \frac{\partial f}{\partial x}(x,y)=\cos (x) +a.
    \cos (x) +a=0 \Leftrightarrow \cos (x)=-a which never happens since a>1. Therefore f doesn't have a minimum, so the affirmation is false.
    Am I right?
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  2. #2
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    Looks good to me.
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