184quiz1solns

184quiz1solns - Math 184 Quiz 1 Solutions 1. f (x) =...

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Unformatted text preview: Math 184 Quiz 1 Solutions 1. f (x) = Solution: 2 f (x) = 3 (x3 - 11) 2 2 f (x) = ( 2 (x3 - 11) 2 ) = 3 ((x3 - 11) 2 ) (by the Constant Multiple Rule) 3 1 1 1 2 x3 -11 . 3 Find f (3). = = 21 3 3 2 (x 21 3 3 2 (x - 11) - 11) -1 2 (x3 - 11) (by the Chain Rule) 3x2 = x2 (x3 - 11) = 9 16 -1 2 -1 2 = 2 x . x3 -11 So, f (3) = 2 3 33 -11 = 9. 4 2. g(x) = Solution: dg dx ( x+1)4 . ( x-1)3 Find dg dx . = d dx (x 2 +1)4 1 (x 2 1 -1)3 = 1 d 2 dx ((x d + 1)4 )(x 2 - 1)3 - (x 2 + 1)4 dx ((x 2 - 1)3 ) 1 1 1 [(x 2 - 1)3 ]2 1 1 1 by the Quotient Rule 1 = d d 4(x 2 + 1)3 dx (x 2 + 1)(x 2 - 1)3 - (x 2 + 1)4 3(x 2 - 1)2 dx (x 2 - 1) 1 1 1 1 (x 2 -1 )6 1 by the Chain Rule (x 2 -1 )6 (The previous line would be ok for your final answer, but I'll simplify a bit more) = x = -1 2 1 = 4(x 2 + 1)3 1 x 2 1 -1 2 (x 2 - 1)3 - (x 2 + 1)4 3(x 2 - 1)2 1 x 2 1 1 1 -1 2 2x -1 2 (x 2 + 1)3 (x 2 - 1)3 - 3 x 2 (x 2 -1 )6 1 1 1 1 1 -1 2 (x 2 + 1)4 (x 2 - 1)2 x = 7 2 -1 2 1 1 (x 2 + 1)3 (x 2 - 1)2 2(x 2 - 1) - 3 (x 2 + 1) 2 (x 2 -1 )6 1 1 3 (x 2 + 1)3 2x 2 - 2 - 2 x 2 - 1 1 1 3 2 (x 2 -1 )4 ( x + 1)3 ( x - 7) 2 x( x - 1)4 1 x = -1 2 (x 2 + 1)3 1 1 1 1 2 2x - 7 2 (x 2 -1 )4 = 1 ( x x + 1)3 2x - ( x - 1)4 1 = ...
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