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    Evaluating Functions using Derivatives

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    Let f be a function that is differentiable for all real numbers. The table gives the values of f and its derivative f' for selected points x in the closed interval -1.5<or equal x< or equal 1.5. The second derivative of f has the property that f''(x)>0 for -1.5<or equalx<or equal 1.5

    Find a positive real number r having the property that there must exist a value c with 0 < c < 0.5 and f''(c) = r. Give reasons for your answer.

    x -1.5 -1.0 -0.5 0 0.5 1.0 1.5
    f(x) -1 -4 -6 -7 -6 -4 -1
    f'(x) -7 -5 -3 0 3 5 7

    © BrainMass Inc. brainmass.com March 4, 2021, 5:48 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/evaluating-functions-using-derivatives-11827

    Solution Summary

    A function is evaluated using first and second derivatives.

    $2.49

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