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    Continuity proof

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    Let a < b, and f : ]a; b[ in R.
    Assume f is continuous at x0 in ]a; b[ and f(x0) > c
    for some number c in R.
    Prove that there is delta > 0 such that
    f(x) > c for all x in ]x0 - delta; x0 + delta[.

    Hint;
    what would happen if, for every delta>0 there were xdelta in ]x0 - delta; x0 + delta[ with f(xdelta)=< c?

    © BrainMass Inc. brainmass.com October 9, 2019, 10:22 pm ad1c9bdddf
    https://brainmass.com/math/discrete-math/continuity-proof-numbers-218223

    Solution Preview

    Please see the attachment.

    Proof:
    From the condition, we know that is ...

    Solution Summary

    This provides an example of a proof regarding a continuous function.

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