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Unformatted text preview: f satisFes f (0) = 2 and f ( x ) = e7 x 2 . ±ind the linear approximation for f (0 . 04). 4. (8 points) Let f ( x ) = x + 2 √ x 2 + 2 . Then, f ( x ) =2( x1) ( x 2 + 2) 3 2 and f 00 ( x ) = 2(2 x 23 x2) ( x 2 + 2) 5 2 . (a) By evaluating the appropriate limit(s), fnd the horizontal asymptote(s) oF the graph oF f . (b) Determine the interval(s) on which the graph oF f is concave up and the interval(s) on which the graph oF f is concave down. 5. (6 points) Compute the derivatives of the following functions. You need not simplify the resulting expression. (a) (2 points) f ( x ) = e sin(5 x ) (b) (4 points) g ( x ) = ln ( x 4 + 2 x 2 + 1) 3 √ x 2 + 4 ( x 2 + x + 1) 4 ! 6. (6 points) A certain function g satisFes g (1) = 6 and its derivative g satisFes 2 ≤ g ( x ) ≤ 5 for 1 ≤ x ≤ 6. What is the smallest possible value of g (6) and what is the largest possible value of g (6)? Justify your answer and indicate which theorem you used....
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 Fall '08
 Yacobi
 Derivative, smallest possible value, certain function, largest possible value

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