Let f: RR be defined by f(x, y) = x xy - xy + y. -...

 

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Let f: RR be defined by f(x, y) = x xy - xy + y. - a) Which obvious symmetry property does f have? What can you conclude from this about the graph and the contours of f? b) Determine all critical points of f and their types. Hint: There are 5 critical points. c) Does f have a global extremum? d) Determine the extrema of f on the unit square Q = {(x, y) = R; 0 x, y 1}. Let f: RR be defined by f(x, y) = x xy - xy + y. - a) Which obvious symmetry property does f have? What can you conclude from this about the graph and the contours of f? b) Determine all critical points of f and their types. Hint: There are 5 critical points. c) Does f have a global extremum? d) Determine the extrema of f on the unit square Q = {(x, y) = R; 0 x, y 1}.