My book reads as follows:(adsbygoogle = window.adsbygoogle || []).push({});

"This is an entirely elementary algebraic formula concerning a polynomial in x or order n, say

[tex] f(x) = a_0 + a_1x + a_2x^2 + ... + a_nx^n [/tex].

If we replace x by a + h = b and expand each term in powers of h, there results immediately a representation of the form [tex] f(a+h) = c_0 = c_1h + c_2h^2 + ... + c_nh^n [/tex].

Taylor's formula is the relation: [tex] c_v = \frac{1}{v!}f^v(a) [/tex], for the coefficients c_v in terms of f and its derivatives at x = a. To prove this fact we consider the quantity h = b - a as the independent variable, and apply the chain rule which shows that differentiation with respect to h is the same as differentiation with respect to b = a + h."

I don't get how f'(h) = f'(a + h)?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

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!

# Proof of Taylor's formula for polynomials

Loading...

Similar Threads for Proof Taylor's formula |
---|

B Proof of a limit rule |

I Taylor expansion of f(x+a) |

B Proof of quotient rule using Leibniz differentials |

B Don't follow one small step in proof |

**Physics Forums | Science Articles, Homework Help, Discussion**