MATH 131 Final: MATH131 BOYLE-M SPRING2016 ALL-SECTION FINALEXAM SOLUTIONS

• School: University of Maryland
• Department: Mathematics
• Course: MATH 131
• Professor: All

Document Summary

L(x, y) = f (7, 2) + (1)(x 7) + ( 3)(y 2) = 0 + (1)(x 7) + ( 3)(y 2) , f (6. 9, 2. 06) = l(6. 9, 2. 06) = (1)( . 1) + ( 3)(. 06) = . 28 . (b) let f (x, y) = x2 + y2. Duf (1, 2) is the directional derivative of f at (1, 2) in the direction of a unit vector u. Find the unit vector u which gives the largest value for duf (1, 2). and therefore. This u is the unit vector in the direction of the gradient vector. The gradient vector (2x, 2y) at (1, 2) is 2(1, 2). The corresponding unit vector is u = (1/ 5, 2/ 5): let f (x, y) = ey(x2 +y). At each, determine whether f has a local maximum, local minimum or saddle point. We have fx = 2xey fy = ey(x2 + y) + ey = ey(x2 + y + 1) .