Differentiable function - Revision history

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BradleyS at 04:55, June 19, 2011

2011-06-19T04:55:49Z

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2008-12-06T03:13:33Z

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Fox at 02:15, February 20, 2008

2008-02-20T02:15:21Z

Aschlafly: 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: : $\frac{f(x) - f...$

2007-12-25T16:13:57Z

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...

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(a)}{(x - a)}</math>

approaches a limiting value that we call the derivative of the function f(x) at ''x=a''.
[[category:mathematics]]
[[category:calculus]]

@@ Line 3: / Line 3: @@
 :<math>\frac{f(x) - f(a)}{(x - a)}</math>
-approaches a [[limit]]ing value that we call the [[derivative]] of the function f(x) at ''x=a''.
+approaches a [[limit]]ing value that we call the [[Derivative (calculus)|derivative]] of the function f(x) at ''x=a''.
 There is also the more rigorous <math>\epsilon-\delta</math> definition: a function f is said to be differntiable at point ''a'' if ∀<math>\epsilon>0</math> ∃<math>\delta>0</math> such that if

← Older revision		Revision as of 14:43, June 27, 2016
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−	[[~~category~~:~~calculus~~]]	+	[[Category:Calculus]]

← Older revision		Revision as of 04:55, June 19, 2011
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	approaches a [[limit]]ing value that we call the [[derivative]] of the function f(x) at ''x=a''.		approaches a [[limit]]ing value that we call the [[derivative]] of the function f(x) at ''x=a''.
		+
		+	There is also the more rigorous <math>\epsilon-\delta</math> definition: a function f is said to be differntiable at point ''a'' if ∀<math>\epsilon>0</math> ∃<math>\delta>0</math> such that if
		+
		+	::<math> \|x - a\| < \delta\,</math>
		+
		+	then
		+
		+	::<math>\|\frac{f(x) - f(a)}{x-a} - f'(a) \| < \epsilon \,</math>.
		+
		+

	[[category:calculus]]		[[category:calculus]]

@@ Line 1: / Line 1: @@
-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>
-approaches a limiting value that we call the [[derivative]] of the function f(x) at ''x=a''.
+approaches a [[limit]]ing value that we call the [[derivative]] of the function f(x) at ''x=a''.
-[[category:mathematics]]
 [[category:calculus]]