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 -1.50 for -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