Continuity and Uniform Continuity - University of …

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the same as the slope f0(c) of the tangent point at the intermediate point (c;f(c)).) If x 1 and x 2 lie in some interval Sand jf0(c)j Mfor all c2S we conclude that the Lipschitz inequality (1) holds on S. We don’t want to use the Mean Value Theorem without rst proving it, but we certainly can

  Value, Intermediate, Theorem, Value theorem, The intermediate