Critical points + 2nd derivative test: Multivariable calculus

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I discuss and solve an example where the location and nature of critical points of a function of two variables is sought. The method is to calculate the partial derivatives, set them to zero and then solve to find the critical points. The critical points are then classified by employing the 2nd derivative test for functions of two variables.

Such an example is seen in 2nd year university mathematics subjects.