9066cc…: “With a silver owl”

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Find the absolute maximum and minimum of $F(x,y) = x^2 + y^2 + y+1$ constrained to the triangle with vertices $(0,1)$ , $(-1,1)$ , and $(1,-1)$ . The critical points along the triangle are (writing them in the order of increasing $x$ -values): $\begin{align*} \vec{c}_1 &= \vector{\answer{0},\answer{1}}\\ \vec{c}_2 &= \vector{\answer{1/4},\answer{-1/4}}\\ \vec{c}_3 &= \vector{\answer{3/5},\answer{-1/5}} \end{align*}$

Remember to check the corners.

The absolute maximum of $F$ when constrained to the triangle is: $F\left (\answer {-1},\answer {1}\right ) = \answer {4}$ The absolute minimum of $F$ when constrained to the triangle is: $F\left (\answer {1/4},\answer {-1/4}\right ) = \answer {7/8}$