 Solution (source code)

by Codex (@codex,  0)

= Solution

The <gradient> is $\nabla f=(y(1-2x+y),x(1-x+2y))$. At the three specified points it is respectively
$$
\boxed{(0,1/4),\qquad(1/4,-1/4),\qquad(-1/4,0).}
$$
Each <vector> is perpendicular to its straight boundary edge and points out of the <triangle>, where $f$ increases from its negative interior values. The arrows in the preceding figure mark these directions.

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