document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170706>Question 1170706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this question.<BR>\n" );
document.write( "Determine the intervals of increasing and decreasing for each of the following functions.<BR>\n" );
document.write( "a)f(x)=x^3-3x^2-9x+4<BR>\n" );
document.write( "b)f(x)=5+36x-3x^2-2x^3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795636 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=795636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=x^3-3x^2-9x+4<BR>\n" );
document.write( "derivative is 3x^2-6x-9<BR>\n" );
document.write( "set equal to 0, and divide by 3 so x^2-2x-3=0=(x-3)(x+1)<BR>\n" );
document.write( "so critical points are at x= -1 and x=3<BR>\n" );
document.write( "when x < -1, the function gets more negative, therefore, from (-oo, -1) the function is increasing,<BR>\n" );
document.write( "from -1 < x < 3 it is decreasing,<BR>\n" );
document.write( "and from (3, oo) it is increasing. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-30%2C30%2Cx%5E3-3x%5E2-9x%2B4%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-30%2C30%2Cx%5E3-3x%5E2-9x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "f(x)=-2x3-3x^2+36x+5<BR>\n" );
document.write( "f'(x)=-6x^2-6x+36 set equal to 0 divide by -6 and x^2+x-6=0 <BR>\n" );
document.write( "x^2+x-6=0<BR>\n" );
document.write( "x=(x+3)(x-2)<BR>\n" );
document.write( "critical points are x=-3, 2<BR>\n" );
document.write( "so it is decreasing on the interval (-oo, -3),<BR>\n" );
document.write( "increasing on the interval (-3, 2),<BR>\n" );
document.write( "and decreasing on the interval (2,  oo)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-8%2C3%2C-80%2C80%2C5%2B36x-3x%5E2-2x%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-8%2C3%2C-80%2C80%2C5%2B36x-3x%5E2-2x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The term with the highest power is what drives the function at infinity.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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