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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

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Solution Summary

A function is evaluated using first and second derivatives.

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