Write out the work on paper and make sure to put down all calculation.

12. 5 points Consider f (x, y) = (x - 1)2+y+1 Find the critical point(s), and determine mix, max, or saddle point(s). Find Vf. Calculate the Hessian matrix. Is f concave, convex, or neither?5 points In their formal study of models of group interaction, Bonacich and Bailey (1971) looked at linear and nonlinear systems of equations (their interest was in mod- els that include factors such as free time, psychological compatibility, friendliness, and common interests). One of their conditions for a stable system was that the determi- nant of the matrix: r a O B = O 'r a 1 O r must have a positive determinant for values of r and a. What is the arithmetic rela- tionship that must exist between a and r for this to be true? \f