MAT 228 Midterm: F05mt2sol

• School: University of Maine
• Department: Mathematics and Statistics
• Course: MAT 228
• Professor: All

Document Summary

November 22, 2005: (18 pts) suppose the temperature at point (x, y, z) is given by. T (x, y, z) = 3x + y2 + z3. The gradient t (1, 3, 2) points in the direction in which t is increasing most rapidly at (1, 3, 2). Note so she should crawl in the direction of t (1, 3, 2) = h3, 6, 12i . Note that k h2, 2, 1ik = 4 + 4 + 1 = 9 = 3. So a unit vector pointing in the given direction is u = (cid:10) 2. The rate of change in this direction is. Dut (1, 3, 2) = t (1, 3, 2) u = h3, 6, 12i (cid:28)2. = 2 + 4 + 4 = 10: (14 pts) consider the surface de ned by. Find an equation for the tangent plane to the surface at the point (1, 2, 6). F (x, y, z) = 2x3z 3x2y = 6.