Error bounds with approximated M value

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To approximate the value 'M' for the error bound in the Trapezoid Rule when the second derivative cannot be directly found, one can utilize the known second derivative of the error function, erf. The goal is to determine the appropriate value of 'n' to achieve an approximation of erf(1.00) within an error margin of 0.001. Techniques such as numerical estimation or bounding the second derivative can be employed to find 'M'. Understanding the behavior of the error function and its derivatives is crucial for accurate error estimation. This approach ensures that the error bounds are effectively calculated even when direct derivatives are unavailable.
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How do you approximate the value 'M' for the error bound formula for the Trapezoid Rule of a function that the derivative cannot be found?

Error Bound Formula: http://archives.math.utk.edu/visual.calculus/4/approx.2/index.html

I'm trying to figure out the value of n to get erf(1.00) approximated within the error of 0.001?

Error Function: http://en.wikipedia.org/wiki/Error_function

How do i get M(in the error bound formula) when it is not possible to get the second derivative of the error function?
 
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But it IS possible to get the second derivative of erf.
 

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