Critical Points of a Differentiable Function

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Consider the function \[f(x,y) = xy - \dfrac{1}{9} (x^3+y^3).\] The critical points (\((0,0)\) and \((3,3)\)) occur when \(\nabla f = \langle f_x, f_y \rangle = \langle 0, 0 \rangle\). There are no other critical points since \(f(x,y)\) is differentiable for all \(x\) and \(y\).

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Joseph Lo, Created with GeoGebra