What does "Holding $f$ and $x$ fixed" mean, for instance, with $\frac{1}{2h}\left[f(x+h)-f(x-h)\right]$?

Asked Feb 02 '23 at 05:35

Active Feb 02 '23 at 07:18

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Reading on Richardson Extrapolation, in my textbook. The authors state that

Holding $f$ and $x$ fixed we define a function of $h$ by the formula $$\phi(h) = \frac{1}{2h}\left[f(x+h)-f(x-h)\right]$$

I'm unsure what it means to be "Holding" a function and $x$ "Fixed".

Any help on defining these terms "Holding" and "Fixed" is much appreciated, thank you for your time.

edited Feb 02 '23 at 07:18

Blue

asked Feb 02 '23 at 05:35

Nicko Cruz M

1

It just means you are considering the expression as a function of $h$ alone; $f$ is a fixed function and $x$ is a fixed number. – geetha290krm Feb 02 '23 at 05:37
2

To "hold fixed" means "to leave unchanged." – Sean Roberson Feb 02 '23 at 05:37

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