Difference between revisions of "Difference quotient"
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(New page: The Difference quotient is used in Calculus to compute the slope of a secant line through two points on a graph of a function ''f(x)''. :<math>\frac{F(x+\Delta x)-F(x)}{\Delt...) |
Masterbratac (talk | contribs) (mathiness++) |
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| − | :<math>\frac{ | + | :<math>\frac{f(x+\Delta x)-f(x)}{\Delta x}\,\!</math> |
==How the Difference quotient differs from the Derivative== | ==How the Difference quotient differs from the Derivative== | ||
| − | The difference between the [[difference quotient]] and the [[derivative]] is that the [[derivative]] is the value of the [[difference quotient]] as the [[secant line]]s get closer and closer to the [[tangent line]] | + | The difference between the [[difference quotient]] and the [[derivative]] is that the [[derivative]] is the value of the [[difference quotient]] as the [[secant line]]s get closer and closer to the [[tangent line]]: |
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| + | :<math>f'(x)=\lim _{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}\,\!</math> | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 20:44, September 25, 2007
The Difference quotient is used in Calculus to compute the slope of a secant line through two points on a graph of a function f(x).
- <math>\frac{f(x+\Delta x)-f(x)}{\Delta x}\,\!</math>
How the Difference quotient differs from the Derivative
The difference between the difference quotient and the derivative is that the derivative is the value of the difference quotient as the secant lines get closer and closer to the tangent line:
- <math>f'(x)=\lim _{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}\,\!</math>