Question

Consider the function, ? (?) = 19x^4 + 23x^3 - 20x, Use zero-to-fourth-degree approximation to predict ? (5) using as a base point ? = 3. Compute the relative true percentage error ?? for each approximation. Briefly discuss your results, provide a brief narrative (5 pts.).

Answer 1

We note that means

and higher order derivatives are zero

So that

are the zero to fourth order approximations

With we get the table of true errors as:

n	T_n(5)	error
0	2100	-86%
1	12712	-13%
2	17644	20%
3	18648	27%
4	18954	29%

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