Homework #8

13.10	16. Finding and classifying critical points of a 2-variable function.

13.5    X. Find the absolute max and min of the function 
              f(x,y)= x2 - xy + y2 - 2x - 4y + 5
           on the triangular region with corners (4,0),(0,4),(4,4). 

13.6    43. Partial derivatives can exist where a function is not continuous!    

	 X. This problem is to be done by hand, with all the steps shown.
            Find an approximate solution of the simultaneous nonlinear equations
	       x2 + y2 - xy - 2x - 4y + 5 = 0,
               x2 + y2 - 16 = 0,
            by linearizing the two LHSs at (0,5) (my VERY rough guess at a solution),
            and determining where the linearizations are simultaneously zero.
	    Proceed as follows. Do everything by hand (though you are free
            to check your work with Maple).
	    (a) Find the linearization at (x0,y0) of each of the LHSs of the
                equations above.
	    (b) Now plug in (0,5) for (x0,y0) to obtain
                the linearizations at (0,5).
	    (c) Set the two linearizations = 0, and solve for (x,y).


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