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Unformatted text preview: without the deFnition. 4. () Derive the quotient rule for derivatives from the product rule and the chain rule. 3 continued on next page Name: Student number: 5. () Consider the function f ( x ) = 1 + 1 /x + 1 /x 2 . (i) f p ( x ) =1 x 2 (1+ 1 2 x ). Find the intervals on which f is increasing and the intervals on which f is decreasing. (ii) f pp ( x ) = 1 2 x 3 (1 + 1 3 x ). Find the intervals on which f is concave up and the intervals on which f is concave down. 4 continued on next page Name: Student number: (iii) Find lim x f ( x ) and lim x  f ( x ). (iv) Sketch the graph of y = f ( x ), incorporating all of the above information. 5 continued on next page...
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 Fall '09
 Dr.Lozinski
 Calculus

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