document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912018>Question 912018</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A curve has an equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=xe%5Ex ALIGN=MIDDLE  ALT=\"y=xe%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The curve has a stationary point at P.<BR>\n" );
document.write( "(i)Find,in terms of e, the coordinates of P and determine the nature of this stationary point.<BR>\n" );
document.write( "The normal to the curve at the point Q (1,e) meets the x-axis at R and the y-axis at S.<BR>\n" );
document.write( "(ii)Find in terms of e, the area of the triangle ORS, where O is the origin. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553544 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=553544\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A curve has an equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=xe%5Ex ALIGN=MIDDLE  ALT=\"y=xe%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The curve has a stationary point at P.<BR>\n" );
document.write( "(i)Find,in terms of e, the coordinates of P and determine the nature of this stationary point.<BR>\n" );
document.write( "y' = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex+%2B+x%2Ae%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex+%2B+x%2Ae%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex+%2B+x%2Ae%5Ex+=+0 ALIGN=MIDDLE  ALT=\"e%5Ex+%2B+x%2Ae%5Ex+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "e^x = 0 (Ignore)<BR>\n" );
document.write( "x = -1 is a local minimum<BR>\n" );
document.write( "y = 1/e<BR>\n" );
document.write( "(-1,1/e) is a local minimum<BR>\n" );
document.write( "===============================<BR>\n" );
document.write( "The normal to the curve at the point Q (1,e) meets the x-axis at R and the y-axis at S.<BR>\n" );
document.write( "(ii)Find in terms of e, the area of the triangle ORS, where O is the origin.<BR>\n" );
document.write( "y' = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex+%2B+x%2Ae%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex+%2B+x%2Ae%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y'(1) = 2e<BR>\n" );
document.write( "m of the normal = -1/(2e)<BR>\n" );
document.write( "y - e = (-1/2e)*(x - 1) = -x/(2e) + 1/(2e)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%2F%282e%29+%2B+%282e%5E2+%2B+1%29%2F%282e%29 ALIGN=MIDDLE  ALT=\"y+=+-x%2F%282e%29+%2B+%282e%5E2+%2B+1%29%2F%282e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> S((2e^2 + 1)/(2e),0)<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%2F%282e%29+%2B+%282e%5E2+%2B+1%29%2F%282e%29+=+0 ALIGN=MIDDLE  ALT=\"y+=+-x%2F%282e%29+%2B+%282e%5E2+%2B+1%29%2F%282e%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+%282e%5E2+%2B+1%29+=+0 ALIGN=MIDDLE  ALT=\"-x+%2B+%282e%5E2+%2B+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 2e^2 + 1 --> R(2e^2 + 1,0)<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Area = bh/2<BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282e%5E2+%2B+1%29%2F%282e%29%29%2A%282e%5E2+%2B+1%29%2F2 ALIGN=MIDDLE  ALT=\"%28%282e%5E2+%2B+1%29%2F%282e%29%29%2A%282e%5E2+%2B+1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282e%5E2+%2B+1%29%5E2%2F%284e%29%29 ALIGN=MIDDLE  ALT=\"%28%282e%5E2+%2B+1%29%5E2%2F%284e%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );