document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181425>Question 181425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi guys! How are you all doing tonight? I am having a difficulty solving this problem and forgive me if I post my topic in the wrong section.\r<BR>\n" );
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document.write( "f(x) = xe^x<BR>\n" );
document.write( "a)  Determine the intervals on which f is strictly increasing or decreasing.<BR>\n" );
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document.write( "b)Determine the extreme value of f.<BR>\n" );
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document.write( "c) Determine the intervals of concavity and of convexity and the inflexion points.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136047 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136047\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = xe^x<BR>\n" );
document.write( "a) Determine the intervals on which f is strictly increasing or decreasing.<BR>\n" );
document.write( "f(x) is decreasing for x<-1<BR>\n" );
document.write( "f(x) is increasing for x>-1 (the minimum is at x = -1)\r<BR>\n" );
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document.write( "b)Determine the extreme value of f.<BR>\n" );
document.write( "f(x) = 0 as x approaches -infinity<BR>\n" );
document.write( "f(x) approaches +infinity as x increases\r<BR>\n" );
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document.write( "c) Determine the intervals of concavity and of convexity and the inflexion points.<BR>\n" );
document.write( "f'(x) = xe^x + e^x<BR>\n" );
document.write( "e^x(x+1) = 0 (1st derivative = 0)<BR>\n" );
document.write( "x = -1 is a minimum<BR>\n" );
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document.write( "f'' = xe^x + 2e^x<BR>\n" );
document.write( "e^x(x+2) = 0 (2nd derivative = 0)<BR>\n" );
document.write( "x = -2 is the point of inflection\r<BR>\n" );
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document.write( "You can see this clearly if you DL the software from http://www.padowan.dk/graph/<BR>\n" );
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