MATH 112 Midterm: MATH 112 UW Sp17 Midterm 2 Solution
Document Summary
Math 112, spring 2017, solutions to midterm ii. 1. (a) d dx ln(cid:0)3x2 + 3x + 5(cid:1) = 4 (b) z (cid:0)5x3 x + e2x 8(cid:1) dx = (c) z 2 dx = z 2 x2 + 1 x2. 3 x3/2 + 0. 5e2x 8x + c. M r (x) = 0. 003x2 0. 24x + 3. 072. M r (x) = 0. 006x 0. 24 = 0 so x = 0. 24/0. 006 = 40. (b) where m c (x) = 0: M c (x) = 0. 003x2 + 0. 24x 4 = 0 x = 0. 24 p0. 242 4(0. 003)( 4) So the minimum value is m c(14. 16) = 50. 26. (c) z 45. 0. 001x3 + 0. 12x2 4x + 80 dx (d) pro t is maximized when m r = m c: 0. 001x3 0. 12x2 + 3. 072x + 200 = 0. 001x3 + 0. 12x2 4x + 80. 0 = 0. 24x2 7. 072x 120 x = 41. 51 (the other root is negative) or so.
