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            Paul's Online Notes
            Paul's Online Notes
            Home / Calculus III / Applications of Partial Derivatives / Absolute Minimums and Maximums
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            Section 3-4 : 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.
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