MATH 241 Midterm: MATH241H_HERB-R_SPRING2007_0101_MID_SOL_1

• School: University of Maryland
• Department: Mathematics
• Course: MATH 241
• Professor: ALL

Document Summary

Thus critical points are (2, 0) and (2, 2). fxx = 2, fyy = 6y + 6, fxy = 0 so d = 12y + 12. At (2, 0), d = 36 > 0 and fxx = 2 > 0 so (2, 0) is a relative min. At (2, 2), d = 12 < 0 so (2, 2) is a saddlepoint: fx = 2x + 1 = 0 if x = 1/2. fy = 2y = 0 if y = 0. Thus ( 1/2, 0) is a critical point inside the region. On the boundary, 2x + 1 = (2x), 2y = (4y), and x2 + 2y2 = 9. Using the second equation, y = 0 or = 1/2. Thus (3, 0) and ( 3, 0) are critical points. If = 1/2, then 2x + 1 = x so x = 1. Thus ( 1, 2) and ( 1, 2) are critical points.