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    Differentiability and Limits

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    Let f: I →ℜ where I is an open interval containing the point c, and let k ∈ ℜ. Prove the following
    1. f is differentiable at c with f ′(x) = k iff lim h→0 [f(c+h) - f(c)]/h=k
    2. If f is differentiable at c with f ′(c) = k , then lim h→0 [f(c+h) - f(c-h)]/2h=k

    © BrainMass Inc. brainmass.com February 24, 2021, 2:22 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/differentiability-limits-16488

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    A proof involving differentiability and limits is provided. The solution is detailed and well presented.

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