Difference between revisions of "Difference quotient"
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| − | The | + | 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)''. |
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==How the Difference quotient differs from the Derivative== | ==How the Difference quotient differs from the Derivative== | ||
| − | The difference between the | + | 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]]: |
:<math>f'(x)=\lim _{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}\,\!</math> | :<math>f'(x)=\lim _{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}\,\!</math> | ||
Revision as of 11:40, July 13, 2016
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>