document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=638252>Question 638252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> good day please help me to solve this problem\r<BR>\n" );
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document.write( "If i have this function :\r<BR>\n" );
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document.write( "f( x ) =1+ 12x – x^3\r<BR>\n" );
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document.write( "which is the minimun relative?<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 #402081 by </B><A HREF=/tutors/aboutme.mpl?userid=Tatiana_Stebko><B>Tatiana_Stebko(1539)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Tatiana_Stebko><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=Tatiana_Stebko><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=402081\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the derivative f'( x )=(1+ 12x – x^3)'=12-3x^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-3x%5E2=0 ALIGN=MIDDLE  ALT=\"12-3x%5E2=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=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=1%2B+12%2A2+%96+2%5E3=17 ALIGN=MIDDLE  ALT=\"f%282%29=1%2B+12%2A2+%96+2%5E3=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=1%2B+12%2A%28-2+%29%96+%28-2%29%5E3=-15 ALIGN=MIDDLE  ALT=\"f%28-2%29=1%2B+12%2A%28-2+%29%96+%28-2%29%5E3=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2, 17) and (-2,-15) are the critical points<BR>\n" );
document.write( "Let use Second derivative test<BR>\n" );
document.write( "the second derivative f''( x )=(12-3x^2)=-6x\r<BR>\n" );
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document.write( "at critical point (2, 17) we find f''(2)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2A2=-12%3C0 ALIGN=MIDDLE  ALT=\"-6%2A2=-12%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so (2, 17) is a relative maximum\r<BR>\n" );
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document.write( "at critical point (-2,-15) we find f''(-2)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2A%28-2%29=12%3E0 ALIGN=MIDDLE  ALT=\"-6%2A%28-2%29=12%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so (-2,-15) is a relative minimum </SPAN>\n" );
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