## 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.