(Solved): Consider the function f(x, y) = 7x + y + xy-7 over the region D = {(x, y) |x| 2, y 2 ...

Consider the function f(x, y) = 7x² + y² + x²y-7 over the region D = {(x, y) |x| ? 2, y ? 2}. a) Find the critical points of f. (1) How many critical points does f have when its domain is not restricted? ol 2 o 3 4 (ii) How many of the critical points are located in D? o all of them O2 of them ol of them Onone of them (iii) Evaluate f at the critical points in D, and give the maximum and minimum of these. (In case of only one critical point in D, these values will be the same.) max f = -7 min f = -7 b) The region D has four boundary lines: left, right, upper and lower. (1) Rewrite the formula for f when restricted to each of these boundary lines. left and right: f(y) = y^2+4y+21 upper: f(x)= 9x^2-3 lower: f(x) = 5x^2-3 Find the maximum and minimum values of f on each boundary segment. max f on left and right: min f on left and right: max fon upper: min f on upper: max f on lower: min f on lower: (iii) Find the absolute maximum/minimum of f over D by comparing the interior maximum/minimum with the boundary maximum/minimum. Absolute maximum of f over D = Absolute minimum of f over D = Your answer: -7 Your answer: -7 Your answer: y2 + 4y +21 Your answer: 9x² – 3 Your answer: 5x²-3 0.5 0.5 1 0.5 0.5 0.5 0.5 0.5 0.5