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Let f(x,y)=x2y22y+1 be subject to the constraint x2+y2 4. (a) Find all candidate points for the locations of the absolute extrema lying inside the...
Let f(x,y)=x2−y2−2y+1 be subject to the constraint x2+y2 ≤4.
(a) Find all candidate points for the locations of the absolute extrema lying
inside the region given by x2 + y2 ≤ 4.
(b) Using the method of Lagrange multipliers, find all candidate points for absolute extreme along the boundary of the region given by x2 + y2 ≤ 4.
(c) Using your answers above, what are the absolute maximum and absolute minimum values of f over the given region? Clearly label and circle the absolute extrema (give the exact function values, not the locations of the extrema).
