Unformatted text preview: MAC1105: Quiz #16 Solutions
July 23, 2010 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back.
1 1. Let f (x) = x . Find f (x+h)-f (x) h f (x+h)-f (x) . h
1 1 x+h - x x 1 1 x+h x x+h - x x+h x-(x+h) x(x+h) -h x(x+h) = h x+1 x-2 . = h = h = h = -1 x(x+h) . 2. Let g(x) = We must set
x+1 x-2 Find the domain of g(x).
[-1, 2] [2, ) x+1 x-2 0. We obtain the following sign chart: (-, -1] + + + Total + + We cannot include the point x = 2, so our domain is (-, -1] (2, ) 3. The graph of f (x) = x4 - 5x2 + 4 is given below: (a) Find all zeros and y -intercept(s). x-intercepts: 2; 1 y -intercepts: 4 (b) Where is f (x) increasing? About (-1.5, 0) (1.5, ). (c) Where does f (x) have a relative minimum?
x 1.5 (d) Where is f (x) < 0?
(-2, -1) (1, 2) 1 ...
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