Answer Happy

Question 2: Find all critical points of the function z = x² - xy + y² + 3x – 2y +1 and determine their character, that is whether there is a local maximum, local minimum, saddle point or none of these at each critical point. In each critical point find the function value in the exact form (don't use a calculator to convert your result to the floating-point format). Rubric: 3 marks for the correct calculation of the partial derivative with respect to x; 3 marks for the correct calculation of the partial derivative with respect to y; 5 marks if the set of equations to determine critical points is found correctly, 6 marks if the critical point is found correctly; 4 marks for the correct calculation of number A; 4 marks for the correct calculation of number B; 4 marks for the correct calculation of number C; 2 marks for the correct calculation of the discriminant D; 4 marks for the correct determination of the nature of the critical point.