To find rate of change you need two instants. how is the rate of change calculated at a particular instant when at least two instants are needed to find it?
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That's why Newton invented the concept of "derivative". You could ask yourself: how can a curve have a local slope, as "slope" is the rise in y value at two different x values. The trick is to use the tangent line, which is the limiting concept of the line linking both points on the curve defining a slope.
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