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### Section 14.4 : Absolute Extrema

1. Find the absolute minimum and absolute maximum of $$f\left( {x,y} \right) = 18{x^2} + 4{y^2} - {y^2}x - 2$$ on the triangle with vertices $$\left( { - 1, - 1} \right)$$, $$\left( {5, - 1} \right)$$ and $$\left( {5,17} \right)$$.
2. Find the absolute minimum and absolute maximum of $$f\left( {x,y} \right) = 2{x^3} - 4{y^3} + 24xy$$ on the rectangle given by $$0 \le x \le 5$$, $$- 3 \le y \le - 1$$.
3. Find the absolute minimum and absolute maximum of $$f\left( {x,y} \right) = {x^2} - {y^2} + xy - 5x$$ on the region bounded by $$y = 5 - {x^2}$$ and the $$x$$-axis.