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    Fundamental differential equation analysis

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    If I be an open interval containing the point x. (x0) and suppose that the function f:I->R has two derivatives. Prove that

    lim as h->0 (f(x.+h) - 2f(x.) + f(x.-h))/ h^2 = f"(x.)

    © BrainMass Inc. brainmass.com March 4, 2021, 5:45 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/fundamental-differential-equation-analysis-9565

    Solution Preview

    By forward difference
    f"(x.)= (f'(x+h)-f'(x))/h ...

    Solution Summary

    The expert provides a proof using forward difference.

    $2.49

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