\( x,y\le \pi/3,f(x,y)=1+\cos xy -\cos x-cos y \)
\( f(x,0)=1-\cos x>0, f(0,y)=1-\cos y>0 \)
\( f_x'(x,y)=\sin x -y\sin xy\begin{cases}\ge 0 &\text{ , } y<1\\ =0 &\text{ , } y=1\\ \le 0 &\text{ , } y>1\end{cases} \)
\( f_y'(x,y)=\sin y -x\sin xy\begin{cases}\ge 0 &\text{ , } x<1\\ =0 &\text{ , } x=1\\ \le 0 &\text{ , } x>1\end{cases} \)
\( 0<x<1, f(x,y)>f(x,0)>0 \).
\( x>1, f(x,y)>f(x,\pi/3)>f(\pi/3,\pi/3)>0 \)
