4b00d3…: “Ahead of the quiet sphere”

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Let $F:\R ^2\to \R$ be a differentiable function that is roughly described by the following table of values:

Consider the closed set defined by: $\vecl (t) = \vector {-1,1}+t\vector {3,3}$ as $t$ runs from $0$ to $1$ . Find the absolute extrema on this set. The absolute maximum of $F$ when constrained to the closed set is: $F\left (\answer {-1},\answer {1}\right ) = \answer {3}$ The absolute minimum of $F$ when constrained to the closed set is: $F\left (\answer {1},\answer {3}\right ) = \answer {-12}$