C-Norm of multiple derivatives

Question

We're calculating Trapezoid and Simpson's rule estimates for definite integrals.  For the error, we need the C-norm of the first - fourth derivatives.  How do I enter this into Mathematica?  As of right now I've been using other calculators to find the max value of the derivatives on an interval.

Daniel Huber · Accepted Answer

It would help if you put a more precise question.
I assume in the following, that you are looking for the maximum of a function and its derivatives over some interval.
As an example I choose "Sin" and the interval {-1,1}. With this assumptions:
f[x_] = Sin[x];
funs = Through[{f, f', f'', f''', f''''}[x]];
Print["MaxValues= ", MaxValue[{#, -1 <= x <= 1}, x] & /@ funs // N]
Plot[funs, {x, -1, 1}, PlotTheme -> "Detailed"]

C-Norm of multiple derivatives

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