document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005663>Question 1005663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the tangent line to the graph of<BR>\n" );
document.write( " f(x)=(x^3+1)/(x^2+x+1) at the point whose x-coordinate is 1<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 #621865 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The slope of the tangent line is equal to the value of the derivative at that point.<BR>\n" );
document.write( "So first find the derivative using the quotient rule.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdx=%28%28x%5E2%2Bx%2B1%29%283x%5E2%29-%282x%2B1%29%28x%5E3%2B1%29%29%2F%28x%5E2%2Bx%2B1%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I won't bother to simplify since we're doing an evaluation,<BR>\n" );
document.write( "So when, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=df%2Fdx=%28%281%5E2%2B1%2B1%29%283%281%29%5E2%29-%282%281%29%2B1%29%281%5E3%2B1%29%29%2F%281%5E2%2B1%2B1%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%283%283%29-3%282%29%29%2F%283%29%5E2 ALIGN=MIDDLE  ALT=\"m=%283%283%29-3%282%29%29%2F%283%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%289-6%29%2F9 ALIGN=MIDDLE  ALT=\"m=%289-6%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1%2F3 ALIGN=MIDDLE  ALT=\"m=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then find the value of the function at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%5E3%2B1%29%2F%281%5E2%2B1%2B1%29=2%2F3 ALIGN=MIDDLE  ALT=\"y=%281%5E3%2B1%29%2F%281%5E2%2B1%2B1%29=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the point-slope form of a line,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2%2F3=%281%2F3%29%28x-1%29 ALIGN=MIDDLE  ALT=\"y-2%2F3=%281%2F3%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2%2F3=%281%2F3%29x-1%2F3 ALIGN=MIDDLE  ALT=\"y-2%2F3=%281%2F3%29x-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x%2B1%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x%2B1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=des1.JPG\">.<BR>\n" );
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