Problem 3. The surface of a dome to be installed on the roof a house can be modelled through the function of two variables f (x,y)=4-x² - y². With respect to the height of the dome, only consider the positive part of the function to be above the house, i.e., (f (x, y) 20). a. Find the domain of the function considering the previously mentioned constraint. b. Graph in the xy plane the level curves corresponding to c= {0, 1, 2, 3, 4 }. c. Find all first and second order partial derivatives. d. Find the coordinate (xy) of the highest point of the dome. Prove why this is in fact the maximum point. e. Find the range of the function, considering the initial constraint (f (x,y)20).

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