Difference Quotient

Pronunciation: /ˈdɪf ər əns ˈkwoʊ ʃənt/ ?

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The difference quotient is the slope of a secant line through two points of a curve.[1]

In the difference equation, h is the change in x and f(x+h)-f(x) is the change in f(x).

The importance of the difference quotient is that it is at the base of calculus. As the two points grow closer together, the closer the slope of the secant line is to the slope of the curve. This gives the expression at the base of calculus:

limit as h approaches zero of (f(x+h)-f(x))/h


  1. Smith, William Benjamin. Infinitesimal Analysis, Volume 1, pp 9-10. The Macmillan Company, 1898. (Accessed: 2010-01-23). http://www.archive.org/stream/infinitsimalanly01willrich#page/n32/mode/1up/search/difference+quotient.
  2. Kuratowski, Kazimierz. Introduction To Calculus, pp 138-140. Translated from Polish by Julian Musielak. Addison-Wesley Publishing Company Inc., 1962. (Accessed: 2010-01-23). http://www.archive.org/stream/introductiontoca033502mbp#page/n143/mode/1up/search/difference+quotient.

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Difference Quotient. 2010-01-23. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/differencequotient.html.


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2010-01-23: Added "References" (McAdams, David.)
2008-12-05: Initial version (McAdams, David.)

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