document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098878>Question 1098878</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the function f(x) = xe^x<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(a) State the domain of f.<BR>\n" );
document.write( "(b) Find the vertical asymptotes and horizontal asymptotes of the curve y(x) = f(x), if exist.<BR>\n" );
document.write( "(c) Find the stationary points of the curve y(x) = f(x) and use the second derivative test to determine their nature.<BR>\n" );
document.write( "(d) Find the points of inflection.<BR>\n" );
document.write( "(e) Determine the x&#8722; and y&#8722; intercepts.<BR>\n" );
document.write( "(f) Sketch the curve using known information.<BR>\n" );
document.write( "(g) State the range of f. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713291 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=713291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=x*e^x<BR>\n" );
document.write( "A)domain is all x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C2%2C-10%2C10%2Cx%2Ae%5Ex%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C2%2C-10%2C10%2Cx%2Ae%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B)Horizontal asymptote is 0-, as x approaches -oo.  No vertical asymptotes.<BR>\n" );
document.write( "C) derivative is x*e^x+e^x.  Set it equal to 0 and e^x(x+1)=0 and x=-1, stationary point at (-1, -e^(-1)) or (-1, -1/e).  <BR>\n" );
document.write( "D) Inflection point is derivative of e^x*(x+1). This is e^x+(x+1)^e^x=e^x(x+2)<BR>\n" );
document.write( "Set that equal to 0, and x=-2, so infection point is (-2, -2/e^2)<BR>\n" );
document.write( "E) when y=0 x=0, so (0, 0) is y intercept and x intercept.<BR>\n" );
document.write( "G. Range is (-1/e, +oo)<BR>\n" );
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