MTH 162 Midterm: MTH 162 University of Rochester 162 Midterm 2 Fall 06
31 Jan 2019
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Part a: (16 pts) let (a) (5 points) find the intervals on which f (x) is increasing and decreasing. f (x) = x2 4x + 3 = (x 1)(x 3) Thus, f (x) is concave up x > 2 and concave down x < 2: (14 pts) Let y = x2 2x + 2. 2x2 5x + 3 (a) (7 points) find the vertical asymptotes. y = x2 2x + 2 (2x 3)(x 1) Thus, vertical asymptotes are x = 1 and x = 1. 5 (b) (7 points) find the horizontal asymptotes. lim x x2 2x + 2. A box with a square base and open top must have a volume 32m3. Find the dimensions of the box that minimizes the amount of material used. Let x be the width and y be the height. The surface area of the box will be. We need to di erentiate a(x) and set it equal to 0.
