Suppose $f(x,y) = x e^{-2 x^2 - 2 y^2}.$ Answer the following.

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1. Find the local maxima of $f.$ List your answers as points in the form $(a,b,c)$.
Answer (separate by commas):

2. Find the local minima of $f.$ List your answers as points in the form $(a,b,c)$.
Answer (separate by commas):

3. Find the saddle points of $f.$ List your answers as points in the form $(a,b,c)$.
Answer (separate by commas):

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