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Unformatted text preview: f ( x ) increase and the intervals on which f ( x ) decreases. (a) f ( x ) = r 1 + x 2 2 + x 2 (b) f ( x ) = 2 x 5 / 3 + 5 x 2 / 3 8 (7) Find the critical points of f ( x ) and the local extreme values. (a) f ( x ) = (1x ) 2 (1 + x ) (b) f ( x ) =  x 216  9 (8) Describe the concavity of the graph of f ( x ) and ﬁnd the points of inﬂection (if any). (a) f ( x ) = (1x ) 2 (1 + x ) 2 (b) f ( x ) = 2 cos 2 xx 2 , x ∈ [0 ,π ] 10 (9) Let f ( x ) = x 1 / 3 ( x6) 2 / 3 . Find (a) the intervals on which f ( x ) increases or decreases (b) the local maxima and minima (c) the intervals on which the graph of f ( x ) is concave up and the intervals on which it is concave down (d) the points of inﬂection 11 (10) Let f ( x ) = ax 3 + bx 2 + cx + d such that a 6 = 0. Under what conditions on a , b , and c will f ( x ) have: (a) two local extrema? (b) only one local extremum? (c) no local extrema?...
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 Spring '09
 N/A
 Calculus, #, Mathematical analysis, Extreme value, 4000 miles, 9.8 inches

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