Use graphical software to plot four or five points that happen to generate an interpolating polynomial that exhibits a great deal of oscillations. This piece of software should let you use your computer mouse to click on three or four points that visually appear to be part of a smooth curve. Next it uses Newton’s interpolating polynomial to sketch the curve through these points. Then add another point that is somewhat remote from the curve and refit all the points. Repeat, adding other points. After a few points have been added in this way, you should have evidence that polynomials can oscillate wildly.
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