exists. It is understood that the limit is taken for x + h ∈ I. Thus if x is, say, a left end point of the interval, we consider only values of h >0. We see no reason to limit ourselves to open intervals. If f is differentiable at x, it is obviously continuous at x. If the above limit exists, we call it the derivative of f at x, and denote it by f′(x). If f is differentiable at every point of I, then f′ is a function on I.
KeywordsRational Number Inverse Function Closed Interval Open Interval Chain Rule
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