What is the difference between an interpolated point and an extrapolated point? What assumption is interpolation and extrapolation based on? Which technique is more prone to error?

Question

What is the difference between an interpolated point and an extrapolated point?  What assumption is interpolation and extrapolation based on?  Which technique is more prone to error?

bobpursley · Answer

interpolated: between two known points extrapolated: beyond the last known point extrapolation is generally more prone to error. Both are based on the theory of differentials.

Allie · Answer

What is the theory of differentials?