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140Bquiz8c - 1 MATH 140B QUIZ#8 Due 2 1 Consider the...

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1 MATH 140B QUIZ#8 Due: Oct 29, 2007 [ 2 ] 1. Consider the function f ( x ) = 4 x x 2 + 1 on the interval I = [ - 3 , 3] . Which of the following 3 statements are true? i) f ( x ) = 4(1 - x 2 ) ( x 2 + 1) 2 ii) f has exactly 2 critical points in I . iii) A local maximum occurs at x = 1 , but it is not a global maximum. A) i) only B) ii) only C) i) and ii) only D) i) and iii) only E) All 3 statements are true. [ 2 ] 2. Consider the function f ( x ) = x 8 x - x 2 on the interval I = [0 , 8] . Which of the following 3 statements are true? i) f ( x ) = 2 x ( x - 6) 8 x - x 2 ii) f has 4 critical points in I . iii) The absolute minimum of f occurs at exactly two different x -values in I . A) i) only B) iii) only C) ii) and iii) only D) i) and iii) only E) All 3 statements are true. [ 2 ] 3. Consider the function f ( x ) = sin x 3 - sin x on the interval I = [0 , 2 π ] . Which of the following 3 statements are true? i) f ( x ) = 3 cos x (3 - sin x ) 2 ii) The absolute minimum of f occurs at exactly two different x -values in I . iii) The absolute maximum of f occurs at an endpoint of I A) i) only B) ii) only C) i) and ii) only D)
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