Unformatted text preview: MAC1105: Quiz #16 Solutions
July 23, 2010 In the topright 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 x2 . = h = h = h = 1 x(x+h) . 2. Let g(x) = We must set
x+1 x2 Find the domain of g(x).
[1, 2] [2, ) x+1 x2 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). xintercepts: 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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 Summer '10
 Picklesimer
 Algebra, Following, Pen, The Domain, Sydney, x+h

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