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Computer algebra systems (CAS) such as Derive, Maple and Mathematica are influencing the way we teach mathematics. With the assistance of CAS, we can examine new avenues for exploring old problems, and perhaps gain new insights. For this paper, we take a close look at the fact that the limit of "the secant line" is "the tangent line." We recast this situation in the notation of polynomial approximation and view the secant line as the Newton polynomnial p1(x) of degree one passing through the two points (x0, f(x0) and (x0=h, f(x0=h)). The tangent line is the Taylor polynomial T1(x) = f(x0) + f'(x0) (x-x0).
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