Use a centered difference approximation of O(h²) to estimate the second derivative of the function examined in Prob. 4.13. Perform the evaluation at x = 2 using step sizes of h = 0.2 and 0.1. Compare your estimates with the true value of the second derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion.

Data From Problem 4.13

Use zero- through third-order Taylor series expansions  to predict f (3) for

f(x) = 25x³ − 6x² + 7x − 88

using a base point at x = 1. Compute the true percent relative error ε t for each approximation.