Each of the following functions has at most one critical point. Graph a few level curves and a few gradients and, on this basis alone, decide whether the critical point is a local maximum, a local minimum, a saddle point, or that there is no critical point.

For $f(x, y) = e^{- x^2 - 3 y^2}$, type of critical point: ? Local Maximum Local Minimum Saddle Point No Critical Point

For $f(x, y) = e^{x^2 - 3 y^2}$, type of critical point: ? Local Maximum Local Minimum Saddle Point No Critical Point

For $f(x, y) = x^2+ 3 y^2+ 1$, type of critical point: ? Local Maximum Local Minimum Saddle Point No Critical Point

For $f(x, y) = x^2+ 3 y+ 1$, type of critical point: ? Local Maximum Local Minimum Saddle Point No Critical Point