A function with several critical points

This shows the graph of a function $z = f(x,y) = 4 \cos(x) \cos(y) e^{-(x^2+y^2)/3} $, which has critical points of all three types.

There is a local maximum at $(a,b)=(0,0)$, with value $f(0,0)=4$. Note that the two tangent lines are horizontal, as is the case at all critical points.

There is a local minimum at $(a,b)\approx(2.17,0)$, with value $f(a,b)\approx -0.47$. Note that the two tangent lines are horizontal, as is the case at all critical points.

There is a saddle at $(a,b)\approx(-1.57,-1.57)$, with value $f(a,b)=0$. Note that the two tangent lines are horizontal, as is the case at all critical points.