You are to find the maximum and minimum value of the objective function in the domain d. you should report the max and min values you find and, for each, whether it occurs: (i) at a critical point of the objective function within the interior of the domain d, or (ii) on the boundary of d, where the constraint function has value exactly 1.

If f is differentiable at c and f′(c) = 0, then we call c a critical point or stationary point of f. A point c at which the derivative of f is not defined is called a singular point of f.

Thus we know that the candidates for the location of the extreme values of a continuous function on a closed interval fall into three categories: (a) endpoints of the interval, (b) critical points, and (c) singular points. To determine the extreme values of such a function f, we identify all these points, evaluate f at each one, and identify the largest and smallest values. 

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