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Stationary Points
coburgmaths
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10-25-2009 8:28 PM
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<div style="margin: 12px 0px; font-family: arial; color: #333333; background: #ffffff; border: solid 4px #e5e5e5; width: 100%; clear: left;"><div class="CM_CTB_Content_Wrap" style="margin: 0px; padding: 0px;background-color: #ffffff;"><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content.clipmarks.com/blog_embed/bd698144-27c5-4763-85d5-22a54726cfb0/8D2D66C9-0F12-4DFF-9C3B-1E968C06C191/" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.youtube.com/watch?v=JawmTELoX2U" href="http://www.youtube.com/watch?v=JawmTELoX2U" style="font-size: 11px;">www.youtube.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.youtube.com/watch?v=JawmTELoX2U"><H1>Finding Stationary Points (Part 1)</H1></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.youtube.com/watch?v=JawmTELoX2U"><DIV class="video-mini-title"><A rel="nofollow" title="Finding Stationary Points (Part 2)" href="http://www.youtube.com/watch?v=DYQghsVOK9M&feature=channel">Finding Stationary Points (Part 2)</A></DIV></blockquote><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content7.clipmarks.com/images/clip-icon.gif" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://mathworld.wolfram.com/StationaryPoint.html" href="http://mathworld.wolfram.com/StationaryPoint.html" style="font-size: 11px;">mathworld.wolfram.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://mathworld.wolfram.com/StationaryPoint.html"><table background="undefined" bgcolor=""><tr><TD width="100%" valign="top" align="left"><DIV class="subjectnavbar"> <A href="http://mathworld.wolfram.com/topics/CalculusandAnalysis.html">Calculus and Analysis</A> > <A href="http://mathworld.wolfram.com/topics/Calculus.html">Calculus</A> > <A href="http://mathworld.wolfram.com/topics/MaximaandMinima.html">Maxima and Minima</A> > </DIV> <DIV class="subjectnavbar"> <A href="http://mathworld.wolfram.com/topics/InteractiveEntries.html">Interactive Entries</A> > <A href="http://mathworld.wolfram.com/topics/InteractiveDemonstrations.html">Interactive Demonstrations</A> > </DIV> <TABLE cellspacing="0" cellpadding="0" border="0"><TBODY><TR><TD valign="baseline" class="title"><SPAN class="nowrap">Stationary Point</SPAN></TD></TR><TR><TD valign="top"><SPAN class="nowrap"><IMG width="100%" height="3" alt="" src="http://mathworld.wolfram.com/images/entries/underline.gif" /><IMG width="20" height="3" alt="" src="http://mathworld.wolfram.com/images/entries/underline.gif" /></SPAN></TD><TD><IMG height="15" alt="" src="http://mathworld.wolfram.com/images/spacer.gif" /></TD></TR></TBODY></TABLE></TD></tr></table></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://mathworld.wolfram.com/StationaryPoint.html"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/mathworld.wolfram.com/img/084DAE95-FC8B-40D9-86DC-291E24E57C63" alt="StationaryPoint" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://mathworld.wolfram.com/StationaryPoint.html"><P class="Text"> A point <IMG width="13" height="16" border="0" alt="x_0" class="inlineformula" src="http://mathworld.wolfram.com/images/equations/StationaryPoint/Inline1.gif" /> at which the <A class="Hyperlink" href="http://mathworld.wolfram.com/Derivative.html">derivative</A> of a <A class="Hyperlink" href="http://mathworld.wolfram.com/Function.html">function</A> <IMG width="26" height="14" border="0" alt="f(x)" class="inlineformula" src="http://mathworld.wolfram.com/images/equations/StationaryPoint/Inline2.gif" /> vanishes, </P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://mathworld.wolfram.com/StationaryPoint.html"><table background="undefined" bgcolor=""><tr><TD align="left"><IMG width="64" height="16" border="0" alt=" f^'(x_0)=0. " class="numberedequation" src="http://mathworld.wolfram.com/images/equations/StationaryPoint/NumberedEquation1.gif" /></TD></tr></table></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://mathworld.wolfram.com/StationaryPoint.html"><P class="Text"> A stationary point may be a <A class="Hyperlink" href="http://mathworld.wolfram.com/Minimum.html">minimum</A>, <A class="Hyperlink" href="http://mathworld.wolfram.com/Maximum.html">maximum</A>, or <A class="Hyperlink" href="http://mathworld.wolfram.com/InflectionPoint.html">inflection point</A>. </P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://mathworld.wolfram.com/StationaryPoint.html"><P class="CrossRefs"> <SPAN class="crosslinkheader">SEE ALSO:</SPAN> <A class="Hyperlink" href="http://mathworld.wolfram.com/CriticalPoint.html">Critical Point</A>, <A class="Hyperlink" href="http://mathworld.wolfram.com/Derivative.html">Derivative</A>, <A class="Hyperlink" href="http://mathworld.wolfram.com/Extremum.html">Extremum</A>, <A class="Hyperlink" href="http://mathworld.wolfram.com/FirstDerivativeTest.html">First Derivative Test</A>, <A class="Hyperlink" href="http://mathworld.wolfram.com/InflectionPoint.html">Inflection Point</A>, <A class="Hyperlink" href="http://mathworld.wolfram.com/Maximum.html">Maximum</A>, <A class="Hyperlink" href="http://mathworld.wolfram.com/Minimum.html">Minimum</A>, <A class="Hyperlink" href="http://mathworld.wolfram.com/SecondDerivativeTest.html">Second Derivative Test</A> </P></blockquote></div><div style="margin: 0px 6px 6px 4px;"><table style="font-size: 11px;border-spacing: 0px;padding: 0px;" cellpadding="0" cellspacing="0" width="100%"><tr><td style="background:transparent;border-width:0px;padding:0px;"> </td><td align="right" style="background:transparent;border-width:0px;padding:0px;width:107px" width="107"><a href="http://clipmarks.com/share/8D2D66C9-0F12-4DFF-9C3B-1E968C06C191/blog/" title="blog or email this clip"><img src="http://content9.clipmarks.com/images/c2b-foot.png" border="0" alt="blog it" width="107" height="17" style="border-width:0px;padding:0px;margin:0px;" /></a></td></tr></table></div></div>
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