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	<id>https://gradwiki.math.ucr.edu/index.php?action=history&amp;feed=atom&amp;title=007A_Sample_Final_2%2C_Problem_10</id>
	<title>007A Sample Final 2, Problem 10 - Revision history</title>
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	<updated>2026-04-20T18:48:39Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://gradwiki.math.ucr.edu/index.php?title=007A_Sample_Final_2,_Problem_10&amp;diff=4514&amp;oldid=prev</id>
		<title>Kayla Murray: Created page with &quot;&lt;span class=&quot;exam&quot;&gt;Let ::&lt;math&gt;f(x)=\frac{4x}{x^2+1}&lt;/math&gt;  &lt;span class=&quot;exam&quot;&gt;(a) Find all local maximum and local minimum values of &amp;nbsp;&lt;math style=&quot;vertical-align: -4px&quot;...&quot;</title>
		<link rel="alternate" type="text/html" href="https://gradwiki.math.ucr.edu/index.php?title=007A_Sample_Final_2,_Problem_10&amp;diff=4514&amp;oldid=prev"/>
		<updated>2017-12-03T06:31:11Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt;Let ::&amp;lt;math&amp;gt;f(x)=\frac{4x}{x^2+1}&amp;lt;/math&amp;gt;  &amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt;(a) Find all local maximum and local minimum values of  &amp;lt;math style=&amp;quot;vertical-align: -4px&amp;quot;...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt;Let&lt;br /&gt;
::&amp;lt;math&amp;gt;f(x)=\frac{4x}{x^2+1}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt;(a) Find all local maximum and local minimum values of &amp;amp;nbsp;&amp;lt;math style=&amp;quot;vertical-align: -4px&amp;quot;&amp;gt;f,&amp;lt;/math&amp;gt;&amp;amp;nbsp; find all intervals where &amp;amp;nbsp;&amp;lt;math style=&amp;quot;vertical-align: -4px&amp;quot;&amp;gt;f&amp;lt;/math&amp;gt;&amp;amp;nbsp; is increasing and all intervals where &amp;amp;nbsp;&amp;lt;math style=&amp;quot;vertical-align: -4px&amp;quot;&amp;gt;f&amp;lt;/math&amp;gt;&amp;amp;nbsp; is decreasing.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt;(b) Find all inflection points of the function &amp;amp;nbsp;&amp;lt;math style=&amp;quot;vertical-align: -4px&amp;quot;&amp;gt;f,&amp;lt;/math&amp;gt;&amp;amp;nbsp; find all intervals where the function &amp;amp;nbsp;&amp;lt;math style=&amp;quot;vertical-align: -4px&amp;quot;&amp;gt;f&amp;lt;/math&amp;gt;&amp;amp;nbsp; is concave upward and all intervals where &amp;amp;nbsp;&amp;lt;math style=&amp;quot;vertical-align: -4px&amp;quot;&amp;gt;f&amp;lt;/math&amp;gt;&amp;amp;nbsp; is concave downward.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt;(c) Find all horizontal asymptotes of the graph &amp;amp;nbsp;&amp;lt;math style=&amp;quot;vertical-align: -5px&amp;quot;&amp;gt;y=f(x).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt;(d) Sketch the graph of &amp;amp;nbsp;&amp;lt;math style=&amp;quot;vertical-align: -5px&amp;quot;&amp;gt;y=f(x).&amp;lt;/math&amp;gt;&lt;br /&gt;
&amp;lt;hr&amp;gt;&lt;br /&gt;
[[007A Sample Final 2, Problem 10 Solution|'''&amp;lt;u&amp;gt;Solution&amp;lt;/u&amp;gt;''']]&lt;br /&gt;
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[[007A Sample Final 2, Problem 10 Detailed Solution|'''&amp;lt;u&amp;gt;Detailed Solution&amp;lt;/u&amp;gt;''']]&lt;br /&gt;
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[[007A_Sample_Final_2|'''&amp;lt;u&amp;gt;Return to Sample Exam&amp;lt;/u&amp;gt;''']]&lt;/div&gt;</summary>
		<author><name>Kayla Murray</name></author>
	</entry>
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