roman Posted February 28, 2009 Posted February 28, 2009 there is a function which is differentiable continuously on [a,b] . suppose |f'(x)|<1 for all[math] x\epsilon [a,b][/math] prove that there exists 0<=k<1 [math] x_1\epsilon [a,b] [/math] [math] x_2\epsilon [a,b] [/math] that this equation is true [math] |f(x_1)-f(x_2)|<=K|x_1-x_2| [/math]
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