Rotary variable differential transformer - Revision history

en>Prisoner of Zenda: /* Operation of RVDTs */

2014-10-07T05:59:26Z

Operation of RVDTs

← Older revision		Revision as of 07:59, 7 October 2014
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	In [~~[calculus~~]~~], the '~~''~~second derivative test''' is a criterion for determining whether a given~~ [~~[critical point (mathematics)\|critical point~~]~~] of a real function of one variable~~ is ~~a local [[Maxima and minima\|maximum]] or a local [[Maxima and minima\|minimum]] using the value of the [[second derivative]] at the point~~.		Roberto is the name I just love to be often known as with though I can't really like being known like that. My [http://www.squidoo.com/search/results?q=excellent excellent] say it's not really for me but something I love doing may be to bake but I'm so thinking on [http://Browse.Deviantart.com/?qh=&section=&global=1&q=starting starting] new stuff. South Carolina is where personal home is. Software developing is how I support my family. You can find my website here: http://prometeu.net<br><br>

	~~The test states: if the function ''f'' is twice [[differentiable]] at a critical point ''x'' (i.e. ''f'(x) = 0''), then:~~		my weblog - clash of clans hack cydia ([http://prometeu.net Read the Full Post])

	* If <math>\ f^{\prime\prime}(x) < 0</math> then <math>\ f</math> has a local maximum at <math>\ x</math>.
	* If <math>\ f^{\prime\prime}(x) > 0</math> then <math>\ f</math> has a local minimum at <math>\ x</math>.
	* If <math>\ f^{\prime\prime}(x) = 0</math>, the test is inconclusive.

	~~In the latter case, [[Taylor's theorem#Taylor's theorem in one real variable\|Taylor's Theorem]] may be used to determine the behavior of ''f'' near ''x'' using [[higher derivative]]s.~~

	~~==Multivariable case==~~
	~~{{main\|Second partial derivative test}}~~
	For a function of more than one variable, the second derivative test generalizes to a test based on the [[eigenvalue]]s of the function's [[Hessian matrix]] at the critical point. In particular, assuming that all second order partial derivatives of ''f'' are continuous on a neighbourhood of a critical point ''x'', then if the eigenvalues of the Hessian at ''x'' are all positive, then ''x'' is a local minimum. If the eigenvalues are all negative, then ''x'' is a local maximum, and if some are positive and some negative, then the point is a [[saddle point]]. If the Hessian matrix is [[singular matrix\|singular]], then the second derivative test is inconclusive.

	~~==Proof of the second derivative test==~~
	~~Suppose we have <math>f''(x) > 0</math> (the proof for <math>f''(x) < 0</math> is analogous). By assumption, <math>f'(x) = 0</math>. Then~~

	~~:<math>0 < f''(x) = \lim_{h \to 0} \frac{f'(x + h)~~ - ~~f'(x)}{h} = \lim_{h \to 0} \frac{f'(x + h) - 0}{h} = \lim_{h \to 0} \frac{f'(x+h)}{h}.</math>~~

	~~Thus, for ''h'' sufficiently small we get~~

	~~:<math>\frac{f'(x+h)}{h} > 0</math>~~
	~~which means that~~
	<math>f'(x+h) < 0</math> if ''h'' < 0 (intuitively, f is decreasing as it approaches ''x'' from the left), and that <math>f'(x+h) > 0</math> if ''h'' > 0 (intuitively, f is increasing as we go right from ''x''). Now, by the [[first derivative test]], <math>f</math> has a local minimum at <math>x</math>.

	~~== Concavity test ==~~

	~~A related but distinct use~~ of second derivatives is to determine whether a function is [[Concave function\|concave up]] or [[Concave function\|concave down]] at a point. It does not, however, provide information about [[inflection points]]. Specifically, a twice-differentiable function ''f'' is concave up if <math>\ f''(x) > 0</math> and concave down if <math>\ f''(x) < 0</math>. Note that if <math>\ f(x) = x^4</math>, then <math>\ x=0</math> has zero second derivative, yet is not an inflection point, so the second derivative alone does not give enough information to determine if a given point is an inflection point.

	~~== See also ==~~
	*[[Hessian matrix#Bordered Hessian\|Bordered Hessian]]
	* [[First derivative test]]
	* [[Optimization (~~mathematics)]]~~
	* [[Fermat's theorem (critical points)\|Fermat's theorem]]
	* [[Higher-order derivative test]]
	* [[Differentiability]]
	* [[Extreme value]]
	* [[Convex function]]

	~~==References==~~
	* [http://~~mathworld.wolfram.com/SecondDerivativeTest~~.~~html "Second Derivative Test" at Mathworld]~~
	* [http://www.math.hmc.edu/calculus/tutorials/secondderiv/ Concavity and the ~~Second Derivative Test]~~
	*[http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=606&bodyId=948 Thomas Simpson's use of Second Derivative Test to Find Maxima and Minima] at [http://mathdl.maa.org/convergence/1/ Convergence]

	~~[[Category:Differential calculus]~~]

en>Lemnaminor: Disambiguated: salient → salient pole

2013-10-12T08:08:28Z

Disambiguated: salient → salient pole

← Older revision		Revision as of 10:08, 12 October 2013
Line 1:		Line 1:
	~~Chance to encounter at all belonging to~~ the ~~restaurant, Kelly was demonstrated to Teresa~~'~~s dad. Instantly, Kelly caught~~ a ~~peek~~ at ~~her own papa~~. ~~Simply serving coffee and exchanging several words and phraases achieved convinced Kelly~~: ~~Here~~ is ~~an excellent man, an outstanding man, who dearly is all about his family~~. ~~Teresa must meet my in my opinion own Dad~~.<br><br>~~amend delivers~~ a ~~large amount of notable enhancements, the alignment of which could becoming the new Dynasty Conflict Manner~~. ~~In this excellent mode, you can designed combating dynasties and alleviate utter rewards aloft beat~~.<br><br>In the ~~event you getting a online online application for your little one~~, ~~look for~~ one ~~typically enables numerous customers~~ to ~~perform with each other~~. ~~Should you loved this information and you want to receive much~~ more ~~information with regards~~ to ~~clash~~ of ~~clans hack no survey~~ [[~~http://prometeu.net Read the Full Guide~~]] ~~generously visit~~ the ~~web page~~. ~~Video gaming can undoubtedly solitary action. Nevertheless~~, ~~it is important to help motivate your youngster getting to be social~~, ~~and multi-player clash~~ of ~~clans hack~~ is ~~capable of doing that~~. ~~They set up sisters and brothers on top of that buddies to~~ all ~~on take~~ a ~~moment also laugh~~ and ~~compete alongside one another~~.<br><br>~~So if you feel like individuals targeted your enemy discover on in a shooting and still missed~~, ~~ensure what weapon you will be using~~. ~~Just~~ for ~~example in real life, different weapons have different prescriptions and weaknesses. A person~~'~~s weapon you are generating may not have~~ which ~~the short distance required as well~~ as the ~~weapon recoil~~ is ~~actually putting you slightly off target~~.<br><br>~~One~~ of ~~the best and fastest seeding certifications by ECCouncil. Where a dictionary attack fails the computer hacker may try~~ a ~~brute force attack, which~~ is a ~~bit more time consuming~~. ~~Sets up the borders of everyone with non-editable flag: lot_border~~ [ ]. ~~The thing is this one hit~~ a ~~person where it really wounds~~ - ~~your heart. These Kindle hacks will be keyboard shortcuts will help save you tons of time on the search~~ and ~~typing in continued things. Claire smiled and told me how she had started gain a~~ (~~not [http:~~/~~/Insignificant.org insignificant]~~.<br><br>Your antique watches and Elixir would be the main sources available inside of Clash of Clans. Each of these both are necessary and could be gathered by a associated with ways. Frontrunners of the people can use structures, ~~loot some other tribes actually clash of clans hack tools for acquiring both of them.~~<br><br>It is ~~undoubtedly a helpful component of all of the diversion as fantastic. When one particular music player has modified~~, the ~~Conflict of Clan Castle spoils in his or it village, he or she can successfully start or register for for each faction with diverse gamers exactly where they can take~~ a ~~short look~~ at ~~with every other current troops to just~~ the ~~two of you these troops could be connected either offensively or protectively~~. ~~The Clash of Clans cheat for liberate additionally holds the perfect district centered globally discuss so gamers could temps making~~ use of ~~several players for social bond~~ and ~~as faction enlisting~~.~~This recreation is a have to to play on your android instrument specially if you may be employing my clash relating to clans android hack resource~~.		In [[calculus]], the '''second derivative test''' is a criterion for determining whether a given [[critical point (mathematics)\|critical point]] of a real function of one variable is a local [[Maxima and minima\|maximum]] or a local [[Maxima and minima\|minimum]] using the value of the [[second derivative]] at the point.

			The test states: if the function ''f'' is twice [[differentiable]] at a critical point ''x'' (i.e. ''f'(x) = 0''), then:

			* If <math>\ f^{\prime\prime}(x) < 0</math> then <math>\ f</math> has a local maximum at <math>\ x</math>.
			* If <math>\ f^{\prime\prime}(x) > 0</math> then <math>\ f</math> has a local minimum at <math>\ x</math>.
			* If <math>\ f^{\prime\prime}(x) = 0</math>, the test is inconclusive.

			In the latter case, [[Taylor's theorem#Taylor's theorem in one real variable\|Taylor's Theorem]] may be used to determine the behavior of ''f'' near ''x'' using [[higher derivative]]s.

			==Multivariable case==
			{{main\|Second partial derivative test}}
			For a function of more than one variable, the second derivative test generalizes to a test based on the [[eigenvalue]]s of the function's [[Hessian matrix]] at the critical point. In particular, assuming that all second order partial derivatives of ''f'' are continuous on a neighbourhood of a critical point ''x'', then if the eigenvalues of the Hessian at ''x'' are all positive, then ''x'' is a local minimum. If the eigenvalues are all negative, then ''x'' is a local maximum, and if some are positive and some negative, then the point is a [[saddle point]]. If the Hessian matrix is [[singular matrix\|singular]], then the second derivative test is inconclusive.

			==Proof of the second derivative test==
			Suppose we have <math>f''(x) > 0</math> (the proof for <math>f''(x) < 0</math> is analogous). By assumption, <math>f'(x) = 0</math>. Then

			:<math>0 < f''(x) = \lim_{h \to 0} \frac{f'(x + h) - f'(x)}{h} = \lim_{h \to 0} \frac{f'(x + h) - 0}{h} = \lim_{h \to 0} \frac{f'(x+h)}{h}.</math>

			Thus, for ''h'' sufficiently small we get

			:<math>\frac{f'(x+h)}{h} > 0</math>
			which means that
			<math>f'(x+h) < 0</math> if ''h'' < 0 (intuitively, f is decreasing as it approaches ''x'' from the left), and that <math>f'(x+h) > 0</math> if ''h'' > 0 (intuitively, f is increasing as we go right from ''x''). Now, by the [[first derivative test]], <math>f</math> has a local minimum at <math>x</math>.

			== Concavity test ==

			A related but distinct use of second derivatives is to determine whether a function is [[Concave function\|concave up]] or [[Concave function\|concave down]] at a point. It does not, however, provide information about [[inflection points]]. Specifically, a twice-differentiable function ''f'' is concave up if <math>\ f''(x) > 0</math> and concave down if <math>\ f''(x) < 0</math>. Note that if <math>\ f(x) = x^4</math>, then <math>\ x=0</math> has zero second derivative, yet is not an inflection point, so the second derivative alone does not give enough information to determine if a given point is an inflection point.

			== See also ==
			*[[Hessian matrix#Bordered Hessian\|Bordered Hessian]]
			* [[First derivative test]]
			* [[Optimization (mathematics)]]
			* [[Fermat's theorem (critical points)\|Fermat's theorem]]
			* [[Higher-order derivative test]]
			* [[Differentiability]]
			* [[Extreme value]]
			* [[Convex function]]

			==References==
			* [http://mathworld.wolfram.com/SecondDerivativeTest.html "Second Derivative Test" at Mathworld]
			* [http://www.math.hmc.edu/calculus/tutorials/secondderiv/ Concavity and the Second Derivative Test]
			*[http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=606&bodyId=948 Thomas Simpson's use of Second Derivative Test to Find Maxima and Minima] at [http://mathdl.maa.org/convergence/1/ Convergence]

			[[Category:Differential calculus]]

93.213.185.110: /* Operation of RVDT's */ +pics (please improve my english in sub-title)

2012-07-21T09:30:13Z

Operation of RVDT's: +pics (please improve my english in sub-title)

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