The Derivative

Steven G. Krantz
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Steven G. Krantz: Washington University, Department of Mathematics

Chapter Chapter 6 in A Handbook of Real Variables, 2004, pp 71-84 from Springer

Abstract: Abstract Let f be a function with domain an open interval I. If x ∈ I, then the quantity $$ \frac{{f(t) - f(x)}}{{t - x}}$$ measures the slope of the chord of the graph of f that connects the points (x, f(x)) and (t, f(t)). If we let t → x, then the limit of the quantity represented by this “Newton quotient” should represent the slope of the graph at the point x.

Keywords: Local Maximum; Constant Function; Differentiable Function; Open Interval; Chain Rule (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-8176-8128-9_6

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