document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180906>Question 1180906</A>: <I><SPAN STYLE=\"word-break: break-all;\"> F(x) =1/x^2 +18x+84<BR>\n" );
document.write( "a) give the domain of f in interval novation <BR>\n" );
document.write( "b) find the critical numbers<BR>\n" );
document.write( "c) determine intervals where f is increasing and decreasing\r<BR>\n" );
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document.write( "Use the derivative test to determine<BR>\n" );
document.write( "a) relative maxima<BR>\n" );
document.write( "b) relative minima  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811106 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811106\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29+=1%2F%28x%5E2+%2B18x%2B84%29 ALIGN=MIDDLE  ALT=\"F%28x%29+=1%2F%28x%5E2+%2B18x%2B84%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a) give the domain of f in interval novation\r<BR>\n" );
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document.write( "domain:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > all real numbers  (no matter what is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, denominator will not be equal to zero\r<BR>\n" );
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document.write( "in interval novation:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "b) find the critical numbers\r<BR>\n" );
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document.write( "critical points are points where the function is defined and its derivative is zero or undefined\r<BR>\n" );
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document.write( "so, find derivative\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F ALIGN=MIDDLE  ALT=\"F\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%281%2F%28x%5E2+%2B18x%2B84%29%29 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%281%2F%28x%5E2+%2B18x%2B84%29%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=F ALIGN=MIDDLE  ALT=\"F\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282x+%2B+18%29%2F%28x%5E2+%2B+18+x+%2B+84%29%5E2 ALIGN=MIDDLE  ALT=\"-%282x+%2B+18%29%2F%28x%5E2+%2B+18+x+%2B+84%29%5E2\"   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=F ALIGN=MIDDLE  ALT=\"F\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-%282%28x+%2B+9%29%29%2F%28x%5E2+%2B+18+x+%2B+84%29%5E2 ALIGN=MIDDLE  ALT=\"+-%282%28x+%2B+9%29%29%2F%28x%5E2+%2B+18+x+%2B+84%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "equal it to zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+-%282%28x+%2B+9%29%29%2F%28x%5E2+%2B+18+x+%2B+84%29%5E2 ALIGN=MIDDLE  ALT=\"0=+-%282%28x+%2B+9%29%29%2F%28x%5E2+%2B+18+x+%2B+84%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...will be zero if numerator equal to zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+-2%28x+%2B+9%29 ALIGN=MIDDLE  ALT=\"0=+-2%28x+%2B+9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x+%2B+9 ALIGN=MIDDLE  ALT=\"0=x+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=-9 ALIGN=MIDDLE  ALT=\"x+=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c) determine intervals where f is increasing and decreasing<BR>\n" );
document.write( "Use the derivative test to determine\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F ALIGN=MIDDLE  ALT=\"F\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%3E0 ALIGN=MIDDLE  ALT=\"%28x%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > f is increasing<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F ALIGN=MIDDLE  ALT=\"F\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%3C0 ALIGN=MIDDLE  ALT=\"%28x%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > f is decreasing\r<BR>\n" );
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document.write( "in your case<BR>\n" );
document.write( "Increasing:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Decreasing:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity+ ALIGN=MIDDLE  ALT=\"infinity+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a) relative maxima<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29+=1%2F%28x%5E2+%2B18x%2B84%29 ALIGN=MIDDLE  ALT=\"F%28x%29+=1%2F%28x%5E2+%2B18x%2B84%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=-9 ALIGN=MIDDLE  ALT=\"x+=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29+=1%2F%28%28-9%29%5E2+%2B18%28-9%29%2B84%29 ALIGN=MIDDLE  ALT=\"F%28x%29+=1%2F%28%28-9%29%5E2+%2B18%28-9%29%2B84%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29+=1%2F%2881+-162%2B84%29 ALIGN=MIDDLE  ALT=\"F%28x%29+=1%2F%2881+-162%2B84%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29+=1%2F3 ALIGN=MIDDLE  ALT=\"F%28x%29+=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "max at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "b) relative minima\r<BR>\n" );
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document.write( "no global minima found\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-20%2C+5%2C+-5%2C+5%2C+1%2F%28x%5E2+%2B18x%2B84%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-20%2C+5%2C+-5%2C+5%2C+1%2F%28x%5E2+%2B18x%2B84%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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