document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=987875>Question 987875</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+x%5E3+%2B+11+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E3+%2B+11+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+3+ ALIGN=MIDDLE  ALT=\"+a+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Find and simplify the quotient:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28f%28x%29-f%28a%29%29%2F%28x+-+a%29+ ALIGN=MIDDLE  ALT=\"+%28f%28x%29-f%28a%29%29%2F%28x+-+a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =\r<BR>\n" );
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document.write( "Then find the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+++M%5Ba%5D+++ ALIGN=MIDDLE  ALT=\"+++M%5Ba%5D+++\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the line tangent to the graph of f at the point (a, f (a)) <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 #608561 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=608561\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Hello,\r<BR>\n" );
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document.write( "your post was written incorrectly from the Perl's point of view.\r<BR>\n" );
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document.write( "I corrected and saved it.\r<BR>\n" );
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document.write( "You can submit it again with my corrections.<BR>\n" );
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document.write( "OK. &nbsp;Now I am continuing to solve it.\r<BR>\n" );
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document.write( "f(x) - f(a) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%2B11%29 ALIGN=MIDDLE  ALT=\"%28x%5E3%2B11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3%2B11%29 ALIGN=MIDDLE  ALT=\"%28a%5E3%2B11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-a%5E3 ALIGN=MIDDLE  ALT=\"x%5E3-a%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-a%29%2A%28x%5E2+%2B+ax+%2B+a%5E2%29 ALIGN=MIDDLE  ALT=\"%28x-a%29%2A%28x%5E2+%2B+ax+%2B+a%5E2%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=%28f%28x%29+-+f%28a%29%29%2F%28x-a%29 ALIGN=MIDDLE  ALT=\"%28f%28x%29+-+f%28a%29%29%2F%28x-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-a%29%2A%28x%5E2+%2B+ax+%2B+a%5E2%29%29%2F%28x-a%29 ALIGN=MIDDLE  ALT=\"%28%28x-a%29%2A%28x%5E2+%2B+ax+%2B+a%5E2%29%29%2F%28x-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+ax+%2B+a%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+ax+%2B+a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "It is the expression for for the slope of the tangent line to the curve &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+11 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;in vicinity of the point &nbsp;(a,f(a).\r<BR>\n" );
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document.write( "If the point &nbsp;<B>x</B>&nbsp; tends to the point &nbsp;<B>a</B>, &nbsp;then the slope tends to &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+a%5E2+%2B+a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+a%5E2+%2B+a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%5E2 ALIGN=MIDDLE  ALT=\"3a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Thus &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5Ba%5D ALIGN=MIDDLE  ALT=\"M%5Ba%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%5E2 ALIGN=MIDDLE  ALT=\"3a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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