document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183580>Question 1183580</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let  f\left(x\right)=\frac{5}{2}x^2-e^x . Find the value of x for which the second derivative f^{\:ii}\left(x\right) equals zero. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813968 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%285%2F2%29x%5E2-e%5Ex ALIGN=MIDDLE  ALT=\"f%28x%29=%285%2F2%29x%5E2-e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > . \r<BR>\n" );
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document.write( "Find the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > for which the second derivative <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >''<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%29 ALIGN=MIDDLE  ALT=\"%28x+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > equals zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%285%2F2%29x%5E2-e%5Ex+ ALIGN=MIDDLE  ALT=\"f%28x%29=%285%2F2%29x%5E2-e%5Ex+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....first find first derivate\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" > ‘<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29=+5x+-+e%5Ex ALIGN=MIDDLE  ALT=\"%28x%29=+5x+-+e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find second derivate\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >‘‘<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29=+5+-+e%5Ex ALIGN=MIDDLE  ALT=\"%28x%29=+5+-+e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "second derivative <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >''<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%29 ALIGN=MIDDLE  ALT=\"%28x+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > equals zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+-+e%5Ex=0 ALIGN=MIDDLE  ALT=\"5+-+e%5Ex=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+=e%5Ex ALIGN=MIDDLE  ALT=\"5+=e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........take natural log of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5Ex%29=ln%285%29 ALIGN=MIDDLE  ALT=\"ln%28e%5Ex%29=ln%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Aln%28e%29=ln%285%29 ALIGN=MIDDLE  ALT=\"x%2Aln%28e%29=ln%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%29=1 ALIGN=MIDDLE  ALT=\"ln%28e%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=ln%285%29 ALIGN=MIDDLE  ALT=\"x=ln%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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