MATH 141 Midterm: MATH141 ROSENBERG-J FALL2012 0101 MID SOL 1

• School: University of Maryland
• Department: Mathematics
• Course: MATH 141
• Professor: All

Document Summary

Note that i may be open, closed, or half-open, and can possibly extend out to in nity. First of all, f is not de ned at x = 0, so i must be contained in (0, ). X 1, so f (x) = 2x 3 + x 2, which vanishes when 2x 3 + x 2 = 0, f (x) = x 2. 2 + x = 0, x = 2. At this point, f (x) changes sign from negative to positive, so this point is a strict local minimum. (alternatively, one can observe that f (x) = 6x 4. So the interval i can extend up to, but not past, this point, 8 = 1 (b) (10 points) find a formula for f 1(y) (where f has the domain i you found in (a)). 2y (c) (5 points) compute (f 1) (0). (note that f (1) = 0. ) Alternatively (but much harder), f 1(0) = lim y 0.