MATH 1550 : Test3 Solutions

• School: LSU
• Department: Mathematics
• Course: MATH 1550
• Professor: All

Document Summary

Each question is worth 10 points, except for question 9 which is worth 20: find the critical numbers of the function f (x) = x 10 ln x. Solution. f (x) = 10x 11 ln x + x 10 1 x. 1 10 ln x x11 so f (x) = 0 when ln x = 1/10. There is one critical number x = e1/10: find the absolute maximum and the absolute minimum values of the function f (x) = x3 + 48/x on the interval [1, 3]. We have f (x) = 3x2 48/x2, so f (x) = 0 when x4 = 16, or x = 2. The only critical number in [1, 3] is 2. 8 0 (x + 1)(1) x(1) (x + 1)2. 1 (x + 1)2 , so f (x) = (f (8) f (0)/(8 0) when (x + 1)2 = 9, or x = 4 or 2.