Difference between revisions of "Differentiable function"
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| − | A function f(x) is '''differentiable''' at the point ''a'' if and only if, as ''x'' approaches ''a'' (which it is never allowed to reach), the value of the quotient: | + | A [[function]] f(x) is '''differentiable''' at the point ''a'' if and only if, as ''x'' approaches ''a'' (which it is never allowed to reach), the value of the quotient: |
:<math>\frac{f(x) - f(a)}{(x - a)}</math> | :<math>\frac{f(x) - f(a)}{(x - a)}</math> | ||
| − | approaches a | + | approaches a [[limit]]ing value that we call the [[derivative]] of the function f(x) at ''x=a''. |
| − | + | ||
[[category:calculus]] | [[category:calculus]] | ||
Revision as of 03:13, December 6, 2008
A function f(x) is differentiable at the point a if and only if, as x approaches a (which it is never allowed to reach), the value of the quotient:
- <math>\frac{f(x) - f(a)}{(x - a)}</math>
approaches a limiting value that we call the derivative of the function f(x) at x=a.