Consider the function: x, a) = 2332 + y2 1% [a] {4 points) Find the critical points of f, i.e. where Vf = 0 or where one of the partial derivatives doesn't exist. Use the Hessian or its determinant to classif},r each of these critical points. Calculate the value of f at each of these points. (b) {1 point] Is there a guarantee that f attains a global maximum and minimum value on D : {fray}; III :1 3, |y| 5 3}? Which critical points lie within D? (c) {3 points) Find the coordinates and values of the maximum and minimum of f along each part of the boundaryr of D. (d) {1 point] What is the global maximum and minimum value of f on D, and at which coordinates do they occur. (e) (5 points) Now consider the region D' = {(33, y); :32 +y2 <_: which critical points lie within d find the global maximum and minimum of f on>