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Section 14.4 : Absolute Extrema

1. Find the absolute minimum and absolute maximum of $$f\left( {x,y} \right) = 192{x^3} + {y^2} - 4x{y^2}$$ on the triangle with vertices $$\left( {0,0} \right)$$, $$\left( {4,2} \right)$$ and $$\left( { - 2,2} \right)$$. Solution
2. Find the absolute minimum and absolute maximum of $$f\left( {x,y} \right) = \left( {9{x^2} - 1} \right)\left( {1 + 4y} \right)$$ on the rectangle given by $$- 2 \le x \le 3$$, $$- 1 \le y \le 4$$. Solution