Unformatted text preview: review our lecture proof of IET. 4. Let f be a function deﬁned by f ( x ) = x 5 + x 4 + x 3 + x 2 + x + 1. Why does f1 ( x ) exist for all x ∈ (0 , ∞ )? Find the value of ( f1 ) (6). EXERCISES: You do not need to submit these questions but you should make sure that you are able to answer them; 1. Spivak # 10.2, 10.16(a)(b), 11.1, 11.5(i)(iii), 11.9, 12.8, 12.11, 12.16(a), 12.17, 12.19 2. Let g be diﬀerentiable. Find a formula for h ( x ) where h ( x ) = g ( x + g ( x )) + e 2 . 3. Suppose that f is diﬀerentiable at 2 and 4 with f (2) = 2, f (4) = 3, f (2) = π , and f (4) = e , If g ( x ) = f 2 ( √ x ), ﬁnd the value of g (4)....
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 Summer '11
 Katherine
 Math, Optimization, Fermat's theorem, Spivak

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