I just learned interpolation and have been looking through it.
It seems like for every data set, interpolation is possible -- is this true? Is there any cases it is not possible to use interpolation?
Any hints or help on this question will greatly help!!!
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Do you know the tangent function?
You have $\tan 0 = 0$ and $\tan \pi = 0$. Dare to interpolate for $\frac\pi 2$...?
Consider the data set $x_0 = 0$, $y_0 = 0$, $x_1 = 0$, $y_1 = 1$. No function can serve as the interpolation here.