# A unique minimum for a 2 variables function?

• July 12th 2009, 09:37 PM
arbolis
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?
• July 13th 2009, 06:47 AM
HallsofIvy
Looks good to me.