MATH 411 Final: MATH411 BOYLE-M SPRING2013 0101 FINAL EXAM

• School: University of Maryland
• Department: Mathematics
• Course: MATH 411
• Professor: All

Document Summary

Math 411 spring 2013 boyle final exam. Points in rn are column vectors (even if they are typed horizontally). Given part (b), use an appropriate inequality to prove that if u is constrained to have some. Xed positive length r then duf (p) is maximized when u is a positive multiple of f (p): (30 pts) de ne f : r2 r by setting f (x, y) = ex+xy+y2. Compute n(r) for n = 3: (50 pts) let e = {(x, y) r2 : x 0, y 0 and x + y = 1}. De ne f (x, y) = 8x2 + y2. Find all points in e at which f assumes a maximum or minimum. Justify your claims that f assumes extreme values at these points and at no other points: (40 pts) for a pair of real numbers c and d, consider the system of equa- tions x + x2 + ex2y2.