So I just began a course on Linear Algebra, and was curious about how we can estimate derivatives using centered differences: After a few minutes of Research, I find the proof involving something about a truncation error, which led me to the conclusion that when estimating derivatives, the rate of change may determine how accurate the estimation is... so my question is: Why?(adsbygoogle = window.adsbygoogle || []).push({});

That is to say, within the mentioned proof, they say that it's best to avoid low values of "h" when estimating derivatives, because if the derivative doesn't change rapidly, the value may be too close to zero... So in summation-

Why is it important to avoid zeroes in calculation? (In the sense that when estimating derivatives, if a particular value is too small, errors may ensue)

And What characterizes a function that changes "too dramatically"?

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# I Truncation Errors Explanation?

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