Critical Points of a differentiable function

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Consider the function \[f(x,y) = 1+x+y-\dfrac{1}{2}x^2-\dfrac{1}{2}y^2.\] We wish to find the absolute extrema of \(f(x,y)\) in the triangular region with vertices \((0,0)\), \((4,0)\) and \((0,4)\)

The following shows the critical points of \(f(x,y)\) both in the interior and on the boundary of the region as well as the endpoints of the boundary. The maxima and minima may occur at any of these points.

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1. Make sure you have the latest version of Java 7 installed in your computer. Tablets and smartphones are not supported.
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Joseph Lo