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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