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Unformatted text preview: f 1 is continuous on its domain. 2. If f is increasing on its domain, then f 1 is increasing on its domain. 3. If f is decreasing on its domain, then f 1 is decreasing on its domain. 4. If f is differentiable at c and f 1 (c) = 0, then f 1 is differentiable at f(c). The Derivative of an Inverse The Derivative of an Inverse Function Function Let f be a function that is differentiable on an interval I. If f has an inverse function g , then g is differentiable at any x for which f’(g(x)) = 0. )) ( ( ' , )) ( ( ' 1 ) ( ' ≠ = x g f x g f x g Graphs of inverse functions have reciprocal slopes at points (a, b) and (b, a). Look at Figure 5.16 on pg. 334 Look at Example 6 pg. 334. Joke Time Joke Time What do cats eat for breakfast? Mice Krispies What did the canary say when its new cage fell apart? CHEEP CHEEP Where does a sheep go to get a hair cut? To the baa baa shop!...
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 Fall '08
 JARVIS
 Calculus, Inverse Functions, 1 g

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