Changes

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)''.

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)''.

==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]]:

:<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>