140Bquiz7c

# 140Bquiz7c - i f ′′ x = 0 at x = 0 and x = ± √ 3 ii...

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1 MATH 140B QUIZ#7 Version A Date: Oct 19, 2007 The following information pertains to questions 1 through 4 below. Consider the rational function f and its 1st and 2nd derivatives given below: f ( x ) = x x 2 + 1 , f ( x ) = 1 - x 2 ( x 2 + 1) 2 , f ′′ ( x ) = 2 x ( x 2 - 3) ( x 2 + 1) 3 [ 2 ] 1. Which of the following 3 statements are true? i) The domain of f is the set of all x not equal to zero. ii) The graph of f is symmetric in the origin. iii) There is a horizontal asymptote at y = 0 . A) ii) only B) iii) only C) i) and iii) only D) ii) and iii) only E) All 3 statements are true. [ 2 ] 2. Which of the following 3 statements are true? i) The graph of f increases on ( - 1 , 1) ii) The graph of f decreases on ( -∞ , - 1) (1 , ) iii) The graph of f has a maximum at x = 1 and a minimum at x = - 1 . A) i) only B) iii) only C) ii) and iii) only D) i) and iii) only E) All 3 statements are true. [ 2 ] 3. Apply a sign pattern test to f ′′ , or use a table with test points, to decide which of the following 3 statements are true? i) f ′′ (

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Unformatted text preview: i) f ′′ ( x ) = 0 at x = 0 and x = ± √ 3 . ii) f is concave up on (-√ 3 , √ 3) . iii) f has exactly 1 point of inFection. A) i) only B) iii) only C) i) and ii) only D) i) and iii) only E) None of the 3 statements are true. 2 [ 2 ] 4. Which of the following is the graph of f. A) M 10 M 5 5 10 M 0.4 M 0.2 0.2 0.4 B) M 10 M 5 5 10 M 0.4 M 0.2 0.2 0.4 C) M 4 M 2 2 4 M 2 M 1 1 2 D) M 4 M 2 2 4 0.2 0.4 0.6 0.8 1.0 [ 2 ] 5. Consider the function r ( x ) = 2 x + 5-3 x + 4 . Which of the following 3 statements are true? i) r has a vertical asymptote at x = 3 / 4 . ii) r has a horizontal asymptote at y = 2 / 3 . iii) The graph of r is symmetric in the origin. A) ii) only B) iii) only C) ii) and iii) only D) i) and iii) only E) None of the 3 statements are true....
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