Let *p*(*x*) be an interpolation polynomial approximating satisfactorily a given function *f*(*x*) over a certain interval *I*. We may hope that the result of differentiating *p*(*x*) will also satisfactorily approximate the corresponding derivative of *f*(*x*). However, if we observe a curve representing the polynomial approximating and oscillating about the curve representing *f*(*x*), we may anticipate the fact that even though the deviation between *p*(*x*) and *f*(*x*) be small throughout the interval, still the slope of the two curves representing them may differ quite appreciably. Also it is seen that the round-off errors of alternating sign in consecutive ordinates could affect the calculation of the derivative quite strongly if those ...

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