Let f be a function that has derivatives of all orders for all real numbers. Assume f(1)=3, f'(1)=-2, f"(1)=2, and f'''(1)=4(adsbygoogle = window.adsbygoogle || []).push({});

a. Write the second-degree Taylor polynomial for f about x=1 and use it to approximate f(0.7).

b. Write the third-degree Taylor polynomial for f about x=1 and use it to approximate f(1.2).

c. Write the second-degree Taylor polynomial for f', the derivative of f, and x=1 and use it to approximate f'(1.2).

a. T{2}(x) = f(1) + f'(1)(x-1) + f"(1)(x-1)^2/2!

plug in .7 = 3.51

b. T{3}(x) = f(1) + f'(1)(x-1) + f"(1)(x-1)^2/2! + f"'(1)(x-1)^3/3!

plug in 1.2 = 2.64

c. What do I do for c?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Taylor Polynomials

Loading...

Similar Threads for Taylor Polynomials | Date |
---|---|

B Taylor Polynomials and decreasing terms | Mar 15, 2017 |

Difference between Taylor Series and Taylor Polynomials? | Dec 5, 2015 |

Taylor Exansion Series Derivation | Aug 6, 2015 |

Taylor Polynomial of 3rd order in 0 to f(x) = sin(arctan (x)) | Oct 19, 2014 |

Power series absolute convergence/ Taylor polynomial | Aug 9, 2014 |

**Physics Forums - The Fusion of Science and Community**