23: You should get

The Lagrange estimate of the error is

The condition in the maximum is in fact not quite correct. Properly it should be like this. If x > 0, then we take maximum over the interval [0,x]. If x < 0, then we take maximum over the interval [x,0]. Rather then writing everything twice we preferred to simply take maximum over a larger interval that includes both versions, which will sometimes make the maximum unnecessarily large, but it should not hurt our estimates much.

Determine the maximum in the formula.

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