Difference between revisions of "Differentiable function"
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(New page: 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...) |
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:<math>\frac{f(x) - f(a)}{(x - a)}</math> | :<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''. | + | approaches a limiting value that we call the [[derivative]] of the function f(x) at ''x=a''. |
[[category:mathematics]] | [[category:mathematics]] | ||
[[category:calculus]] | [[category:calculus]] | ||
Revision as of 02:15, February 20, 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.