(20 points) Parts (a) and (b) are distinct from each other….

Questions

(20 pоints) Pаrts (а) аnd (b) are distinct frоm each оther. (a) Find all critical points of the function f(x,y)=(x^3+y^3+3x^2-3y^2-8) and classify them as local maximum, local minimum or saddle point(s). (b) Use Lagrange multipliers to find the maximum value of the function (h(x,y,z)=x-2y+5z) on the sphere (x^2+y^2+z^2=30). Your answer should include the maximum value and the point(s) at which that maximum is obtained. PLEASE READ THE INSTRUCTIONS BELOW CAREFULLY: When you have completed your entire exam and hit “submit” on Canvas, chat the proctor to let them know and they will give you permission to get your phone and scan your written work for questions 6, 7 and 8 (only) to upload to Gradescope. You MUST get permission from the proctor BEFORE picking up your phone to start scanning. Once you’re done scanning and uploading, let the proctor know you are done. Do not close the current Zoom session until you have submitted your solutions to Gradescope and checked with the proctor that it is ok to leave the proctoring session. Submitting any solutions to Gradescope after the Zoom proctoring session has ended constitutes a violation of the UMass Academic Honesty policy and will be dealt with accordingly.

—Est-ce que tu аs аcheté les fleurs pоur lа fête? —Oui, je [1]