MATH 211 Quiz: MATH 211 NIU s03Quiz5 6Solution
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Let f (x) = x3 3x + 6. (a) [6 pts] find f (x) and the critical points of f (x). (p 199 #9) f (x) = 3x2 3. 3x2 = 3 x2 = 1 x = 1 (b) [4 pts] find the intervals on which f (x) is increasing and decreasing. The critical points separate the number line into the intervals ( , 1), ( 1, 1), and (1, ). We need to check the sign of the rst derivative at one point in each of the intervals. You could choose 2, 0, and 2 as the points. Then nd the value of the derivative at each point. f ( 2) = 3( 2)2 3 = +9. Conclusion: f (x) is positive when x is in the interval ( , 1), negative when x is in ( 1, 1), and positive when x is in (1, ). There is a link to the graph on the class web page.
