MATH 215 Midterm: exam2f03
Document Summary
You do not need to simplify your answer, but we expect you to know and simplify some basic expressions, like 4 or cos . Please do all your work in this booklet and show all the steps. Some useful trigonometric identities: sin2 + cos2 = 1 sin2 = 2 cos 2 = cos2 sin2 cos2 = 2 sin 2 = 2 sin cos . Find and classify all critical points of the function f (x, y) = 5x2y 2xy2 + 30xy 3. Use lagrange multipliers to determine the dimensions of the storage box of the largest volume that can be pushed into the remote dusty corner of the attic as shown on the picture below. z. Consider the function f (x, y) = x cos(cid:16) y (a 5 pts. ) Using the level curves of this function on the plot below, estimate zzr. 2 (cid:17) over the rectangle r = [0, 4] [1, 3]. your setup).
