Description
Problem 1
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 for each approximation.
Problem 2
Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h2) to estimate the first derivative of the function described in problem 1. Evaluate the derivative at x = 2 using a step sive of h = 0.25. Compare your results with the true value of the derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion.
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