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    Differentiable Functions : Lipschitz and Absolute Values

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    I have a function that is differentiable on [a,b] and I am trying to figure out which scenario is more restrictive:

    a) the function is a Lipschitz function with a Lipschitz constant L in (0,1)

    or

    b) the absolute value of f'(x) is less than one for all x in [a,b]

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    https://brainmass.com/math/graphs-and-functions/differentiable-functions-lipschitz-absolute-values-108682

    Solution Preview

    Answer: (a) is more restrictive.
    Proof:
    I claim that (a) can imply (b).
    Suppose (a) holds. f(x) is a ...

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