While teaching Calculus 2, one of my students asked me the following "Given 3 points $x_1$, $x_2$, $x_3$. Whether there exists one function z = f(x,y) which has exactly 2 extremum and 1 saddle point: 1 local minimum at $x_1$, 1 local maximum at $x_2$, 1 saddle point $x_3$."
Given 3 points $x_1$, $x_2$, $x_3$. Whether there exists one function $z = f(x,y)$ which has exactly 2 extremum and 1 saddle point: 1 local minimum at $x_1$, 1 local maximum at $x_2$, 1 saddle point $x_3$.
I looked it up in Stewart and several other textbooks but have not found an answer. Any suggestions or comments are welcome.
