Consider the function f(x,y) over the domain D enclosed by the 1+ x2 + y² polar curve r =2+ sin²(20). Without using any calculus (i.e. taking any derivatives) (a) find all the local extrema of f, (b) find all the local extrema of f subject to the constraint given by the polar curve, (c) determine the global maximum and minimum values of f on D. Hint: Solve this problem pictorially by considering the level curves of f.

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