Advertisement
Published in:
2004 | OriginalPaper | Chapter
The Derivative
Author : Steven G. Krantz
Published in: A Handbook of Real Variables
Publisher: Birkhäuser Boston
Included in: Professional Book Archive
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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.