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| {{Verifiability|date=August 2011}}
| | Making your computer run swiftly is actually very simple. Most computers run slow considering they are jammed up with junk files, which Windows has to look through each time it wants to find something. Imagine needing to find a book in a library, however, all of the library books are in a big huge pile. That's what it's like for a computer to find anything, whenever your system is full of junk files.<br><br>StreamCI.dll errors are caused by a number of different issues, including which the file itself has been moved on the program, the file is outdated or you have installed some third-party sound motorists that are conflicting with the file. The wise news is the fact that if you want to solve the error you're seeing, you need to look to initially ensure the file & motorists are functioning okay on a PC and also then resolving any StreamCI.dll errors which may be inside the registry of your computer.<br><br>Registry cleaning is important because the registry may receive crowded plus messy when it happens to be left unchecked. False entries send the running program trying to find files plus directories that have long ago been deleted. This takes time plus utilizes valuable resources. So, a slowdown inevitably takes place. It is particularly noticeable whenever you multitask.<br><br>Handling intermittent errors - whenever there is a content to the impact which "memory or difficult disk is malfunctioning", we could place inside unique hardware to replace the defective piece till the actual issue is discovered. There are h/w diagnostic programs to identify the faulty portions.<br><br>In a word, to speed up windows XP, Vista startup, it's quite significant to disable some startup goods plus clean and optimize the registry. You are able to follow the steps above to disable unwanted programs. To optimize the registry, I recommend you utilize a [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities 2014] software. Because it really is quite risky for you to edit the registry by yourself.<br><br>Let's begin with the bad sides first. The initial cost of the product is extremely cheap. But, it only comes with 1 year of updates. After which you need to subscribe to monthly updates. The advantage of that is the fact that ideal optimizer has enough cash and resources to analysis errors. This technique, you're ensured of safe fixes.<br><br>Across the top of the scan results display page you see the tabs... Registry, Junk Files, Privacy, Bad Active X, Performance, etc. Each of these tabs might show we the results of which area. The Junk Files are mostly temporary files like web data, pictures, internet pages... And they are merely taking up storage.<br><br>So in summary, when comparing registry cleaning, make sure the 1 you choose provides you the following.A backup and restore center, fast surgery, automatic deletion center, start-up management, an simple technique of contact plus a funds back guarantee. |
| :''Not to be confused with a [[Fixed point (mathematics)|fixed point]] where x ''='' f''(''x'')''.''
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| {{about|stationary points or critical points of a real-valued function of one real variable|the general notion|Critical point (mathematics)}}
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| [[File:Stationary vs inflection pts.svg|350px|thumb|right|The stationary points are the red circles. In this graph, they are all relative maxima or relative minima.]]
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| In [[mathematics]], particularly in [[calculus]], a '''stationary point''' or '''critical point''' is a point of the [[domain of a function|domain]] of a [[differentiable function]], where the [[derivative]] is zero (equivalently, the [[slope]] of the [[graph of a function|graph]] is zero): it is a point where the function "stops" increasing or decreasing (hence the name). For a differentiable [[function of several real variables|function of several variables]], a '''stationary''' or '''critical point''' is an input (one value for each variable) where all the [[partial derivative]]s are zero (equivalently, the [[gradient]] is zero).
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| The stationary points are easy to visualize on the graph of the function: they correspond to the points on the graph where the [[tangent]] is [[Parallel (geometry)|parallel]] to the ''x''-axis. For function of two variables, they correspond to the points on the graph where the tangent plane is parallel to the ''xy'' plane.
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| ==Stationary points, critical points and turning points==
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| The term ''stationary point of a function'' may be confused with ''[[critical point (mathematics)|critical point]] for a given projection of the graph of the function''. | |
| "Critical point" is more general: a stationary point of a function corresponds to a critical point of its graph for the projection parallel to the ''x''-axis. On the other hand, the critical points of the graph for the projection parallel to the ''y'' axis are the points where the derivative is not defined (more exactly tends to the infinity). It follows that some authors call "critical point" the critical points for any of these projections.
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| A '''turning point''' is a point at which the derivative changes sign.{{cn|date=October 2013}} A turning point may be either a relative maximum or a relative minimum. If the function is differentiable, then a turning point is a stationary point; however not all stationary points are turning points. If the function is twice differentiable, the stationary points that are not turning points are horizontal [[inflection point]]s. For example the function <math>x \mapsto x^3</math> has a stationary point at x=0, which is also an inflection point, but is not a turning point.<ref>{{cite web|title=Turning points and stationary points|url=http://www.teacherschoice.com.au/Maths_Library/Calculus/stationary_points.htm|work=TCS FREE high school mathematics 'How-to Library',|accessdate=30 October 2011}}</ref>
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| ==Classification==
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| {{See also|maxima and minima}}
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| Isolated stationary points of a <math>C^1</math> real valued function <math>f\colon \mathbb{R} \to \mathbb{R}</math> are classified into four kinds, by the [[first derivative test]]:
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| [[Image:Stationary and inflection pts.gif|frame|right|Saddle points (coincident stationary points and inflection points). Here one is rising and one is a falling inflection point.]]
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| * a '''local minimum''' ('''minimal turning point''' or '''relative minimum''') is one where the derivative of the function changes from negative to positive;
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| * a '''local maximum''' ('''maximal turning point''' or '''relative maximum''') is one where the derivative of the function changes from positive to negative;
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| * a '''rising [[inflection point|point of inflection]]''' (or '''inflexion''') is one where the derivative of the function is positive on both sides of the stationary point; such a point marks a change in [[concave function|concavity]]
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| * a '''falling point of inflection''' (or '''inflexion''') is one where the derivative of the function is negative on both sides of the stationary point; such a point marks a change in concavity
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| A point that is either a local minimum or a local maximum is called a local extremum. Similarly a point that is either a global (or absolute) maximum or a global (or absolute) minimum is called a global (or absolute) extremum.
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| By [[Fermat's theorem (stationary points)|Fermat's theorem]], global extrema must occur (for a <math>C^1</math> function) on the boundary or at stationary points.
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| ==Curve sketching==
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| {{Cubic graph special points.svg}}
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| Determining the position and nature of stationary points aids in [[curve sketching]] of differentiable functions. Solving the equation ''f'''(''x'') = 0 returns the ''x''-coordinates of all stationary points; the ''y''-coordinates are trivially the function values at those ''x''-coordinates.
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| The specific nature of a stationary point at ''x'' can in some cases be determined by examining the [[second derivative]] ''f''''(''x''): | |
| * If ''f''''(''x'') < 0, the stationary point at ''x'' is concave down; a maximal extremum.
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| * If ''f''''(''x'') > 0, the stationary point at ''x'' is concave up; a minimal extremum.
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| * If ''f''''(''x'') = 0, the nature of the stationary point must be determined by way of other means, often by noting a sign change around that point.
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| A more straightforward way of determining the nature of a stationary point is by examining the function values between the stationary points (if the function is defined and continuous between them).
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| A simple example of a point of inflection is the function ''f''(''x'') = ''x''<sup>3</sup>. There is a clear change of concavity about the point ''x'' = 0, and we can prove this by means of [[calculus]]. The second derivative of ''f'' is the everywhere-continuous 6''x'', and at ''x'' = 0, ''f''′′ = 0, and the sign changes about this point. So ''x'' = 0 is a point of inflection.
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| More generally, the stationary points of a real valued function ''f'': '''R'''<sup>''n''</sup> → '''R''' are those
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| points '''x'''<sub>0</sub> where the derivative in every direction equals zero, or equivalently, the [[gradient]] is zero.
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| ===Example===
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| At x<sub>1</sub> we have ''f' ''(''x'') = 0 and ''f''''(''x'') = 0. Even though ''f''''(''x'') = 0, this point is not a point of inflection. The reason is that the sign of ''f' ''(''x'') changes from negative to positive.
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| At x<sub>2</sub>, we have ''f' ''(''x'') <math>\ne</math> 0 and ''f''''(''x'') = 0. But, x<sub>2</sub> is not a stationary point, rather it is a point of inflection. This because the concavity changes from concave downwards to concave upwards and the sign of ''f' ''(''x'') does not change; it stays positive.
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| At x<sub>3</sub> we have ''f' ''(''x'') = 0 and ''f''''(''x'') = 0. Here, x<sub>3</sub> is both a stationary point and a point of inflection. This is because the concavity changes from concave downwards to concave upwards and the sign of ''f' ''(''x'') does not change; it stays positive.
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| Assuming that f'(x) < 0, there are no distinct roots. Hence ''f''<nowiki>''</nowiki>(''x'') = ''dy''.
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| ==See also==
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| * [[Optimization (mathematics)]]
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| * [[Fermat's theorem (stationary points)|Fermat's theorem]]
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| * [[Second derivative test]]
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| * [[Higher-order derivative test]]
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| * [[Fixed point (mathematics)]]
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| * [[Saddle point]]
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| ==External links==
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| * [http://www.cut-the-knot.org/Curriculum/Calculus/FourthDegree.shtml Inflection Points of Fourth Degree Polynomials — a surprising appearance of the golden ratio] at [[cut-the-knot]]
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| {{reflist}}
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| [[Category:Differential calculus]]
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| [[de:Extrempunkt]]
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Making your computer run swiftly is actually very simple. Most computers run slow considering they are jammed up with junk files, which Windows has to look through each time it wants to find something. Imagine needing to find a book in a library, however, all of the library books are in a big huge pile. That's what it's like for a computer to find anything, whenever your system is full of junk files.
StreamCI.dll errors are caused by a number of different issues, including which the file itself has been moved on the program, the file is outdated or you have installed some third-party sound motorists that are conflicting with the file. The wise news is the fact that if you want to solve the error you're seeing, you need to look to initially ensure the file & motorists are functioning okay on a PC and also then resolving any StreamCI.dll errors which may be inside the registry of your computer.
Registry cleaning is important because the registry may receive crowded plus messy when it happens to be left unchecked. False entries send the running program trying to find files plus directories that have long ago been deleted. This takes time plus utilizes valuable resources. So, a slowdown inevitably takes place. It is particularly noticeable whenever you multitask.
Handling intermittent errors - whenever there is a content to the impact which "memory or difficult disk is malfunctioning", we could place inside unique hardware to replace the defective piece till the actual issue is discovered. There are h/w diagnostic programs to identify the faulty portions.
In a word, to speed up windows XP, Vista startup, it's quite significant to disable some startup goods plus clean and optimize the registry. You are able to follow the steps above to disable unwanted programs. To optimize the registry, I recommend you utilize a tuneup utilities 2014 software. Because it really is quite risky for you to edit the registry by yourself.
Let's begin with the bad sides first. The initial cost of the product is extremely cheap. But, it only comes with 1 year of updates. After which you need to subscribe to monthly updates. The advantage of that is the fact that ideal optimizer has enough cash and resources to analysis errors. This technique, you're ensured of safe fixes.
Across the top of the scan results display page you see the tabs... Registry, Junk Files, Privacy, Bad Active X, Performance, etc. Each of these tabs might show we the results of which area. The Junk Files are mostly temporary files like web data, pictures, internet pages... And they are merely taking up storage.
So in summary, when comparing registry cleaning, make sure the 1 you choose provides you the following.A backup and restore center, fast surgery, automatic deletion center, start-up management, an simple technique of contact plus a funds back guarantee.