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Unformatted text preview: = ( ) 1, 1, U x x x = < ≥ Thm. 2.1 Differentiability Implies Continuity If f is differentiable at x = c, then f is continuous at x = c. It is possible for a function to be continuous at x = c and not be differentiable at x = c. Thus, continuity does not imply differentiability. OneSided Derivatives l A function y = f(x) is differentiable on a closed interval [a, b] if it has a derivative at every interior point of the interval, and if the limits exist at the endpoints. l The usual relationship between onesided and twosided limits holds for derivatives. A function has a (twosided) derivative at a point iff the function’s righthand and lefthand derivatives are defined and equal at that point. Joke Time What would America be called if we all drove pink cars? A pink carnation! Why should you never play cards in the jungle? It’s full of cheetahs!...
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 Fall '08
 JARVIS
 Calculus, Derivative, Mathematical analysis, Continuous function

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