The Derivative

  • Steven G. Krantz


Let f be a function with domain an open interval I. If xI, 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 tx, then the limit of the quantity represented by this “Newton quotient” should represent the slope of the graph at the point x.


Local Maximum Constant Function Differentiable Function Open Interval Chain Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Steven G. Krantz
    • 1
  1. 1.Department of MathematicsWashington UniversitySt. LouisUSA

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