document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143597>Question 143597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me to answer this question, the directions are: <BR>\n" );
document.write( "determine the intervals of increasing and decreasing.\r<BR>\n" );
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document.write( "f(x)=-2x^3-3x^2+12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104511 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=104511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f'(x)=-6x^2-6x<BR>\n" );
document.write( "Find where it is=0\r<BR>\n" );
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document.write( "0=-6x^2-6x<BR>\n" );
document.write( "0=6x(x+1)<BR>\n" );
document.write( "implies x=0 or x=-1. These are our two critical values. Find out what happens outside and between these two values for the derivative f'.\r<BR>\n" );
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document.write( "f'(-2)=-6(-2)^2-6(-2)=-24+12=-12. It is decreasing from (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,-1).<BR>\n" );
document.write( "f'(-1/2)=-6(-1/2)^2-6(-1/2)=-3/2+3=3/2. It is increasing from (-1,0).<BR>\n" );
document.write( "f(1)=-6-6=-12. It is decreasing from (0,<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( "Plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+-2%2C+2%2C+-20%2C+20%2C+-2x%5E3-3x%5E2%2B12+%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+-2%2C+2%2C+-20%2C+20%2C+-2x%5E3-3x%5E2%2B12+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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