MATH 200 Study Guide - Midterm Guide: Contour Line, Iterated Integral, Unit Vector

• School: UBC
• Department: Mathematics
• Course: MATH 200
• Professor: All

Document Summary

Be sure that this examination has 15 pages. Write your name on top of each page. In case of an exam disruption such as a re alarm, leave the exam papers in the room and exit quickly and quietly to a pre-designated location. Consider a twice di erentiable function f (x, y) illustrated by the contour map on the follow page: (3 points. ) Draw the direction of f at point h on the diagram: (3 points. ) Classify these points as local minima, local maxima, or saddle points: (2 points each. )state whether the following quantities at point e are positive or negative. (a) derivative of f in the direction u = (cid:2) 2, 1(cid:3) (b) dy dx along the level curve f (x, y) = 3 (c) fy (d) fyy. Find the global maximum and global minimum of the function f (x, y) = 2x2 + 3y2 4x 5 on the disk x2 + y2 16.