In this chapter we develop the basic theory of derivatives of real-valued functions of one variable. The geometric motivation of the derivative of f at c is that it is the limit of the slope of lines joining (c, f(c)) to nearby points on the graph of f, as these points approach c, and therefore represents the slope of a “line passing through two consecutive points” of the graph of f, i.e., the tangent line. We can enjoy such language without succumbing to it.
KeywordsPower Series Convex Function Open Interval High Order Derivative Power Series Expansion
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