Kenneth S. answered • 12/27/16
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If (a,b) is a POINT on the graph of function f(x), then, since f(a) = b, the numerator of your expression "N" is always zero. OTHERWISE...
If (a,b) is not on graph of function f, but "a" is in the domain of f, then your expression N equals
b/f(a) - 1, in general, and the sign of N tells you whether the (a,b) point is above (+) or below (-) the point (a,f(a)).
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Stephen M.
tutor
The sign will only tell you if it's above or below as stated if f(a) is positive. If f(a) is negative, it's reversed. Incidentally, the numerator, b - f(a), is all you need to look at to see if (a,b) is above (+) or below (-) and directly gives you the vertical distance. In your example, y(4) = 29, so (4,27) is 2 below the curve. Your expression gives a percentage deviation (if multiplied by 100), which might occasionally be useful (6.8% below in your example). Now, if you're looking for shortest distance between a point and a curve, there are techniques to find that.
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