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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