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Unformatted text preview: N be to guarantee that  f ( x )3  < for all x > N ? We need N 5. Then x > 5 gives  f ( x )3  =  1 /x  = 1 /  x  < 1 / 5. 6. Show that the equation x 4x1 = 0 has at least one real solution in the interval (1 , 2). Let f ( x ) = x 4x1. Then f ( x ) is continuous, f (1) =1, and f (2) = 13. Since1 < < 13, there is at least one c (1 , 2) such that f ( c ) = 0, by the intermediate value theorem. 1 7. Dierentiate the function f ( x ) = 2 x + 1 x + 3 . f ( x ) = ( x + 3) 2(2 x + 1) 1 ( x + 3) 2 = 5 ( x + 3) 2 . 8. Dierentiate the function f ( x ) = xe x . f ( x ) = 1 2 x1 / 2 e x + x 1 / 2 e x = ( 1 2 x1 / 2 + x 1 / 2 ) e x . 9. Find the values of x where the graph of y = x 36 x 2 has a horizontal tangent line. We must nd the values of x where y = 0. Now y = 3 x 212 x = 3 x ( x4), so x = 0 or x = 4. 2...
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 Fall '08
 WILKENING
 Calculus

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