Why is it that we are weighing f1 by the t (which seems to be a fraction representing how far x is from x0)? Why aren't we weighing each f by the x position it corresponds to (f0 by t and f1 by (1-t)?
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Suppose a special case: x = x0, in which t = 0, f(t) = f0. Or you can think it in this way, the closer x is to x0, the more percentage f0 accounts for in the result, the greater (1 - t) is, which makes sense because t is less, as a result of x - x0 is less.
Why is it that we are weighing f1 by the t (which seems to be a fraction representing how far x is from x0)? Why aren't we weighing each f by the x position it corresponds to (f0 by t and f1 by (1-t)?
Suppose a special case: x = x0, in which t = 0, f(t) = f0. Or you can think it in this way, the closer x is to x0, the more percentage f0 accounts for in the result, the greater (1 - t) is, which makes sense because t is less, as a result of x - x0 is less.