document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1826>Question 1826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help!  How do you factor: -4x^3+36x^2-12? It is the prime of f(x)=12x^3-12x+24.  I need to find the intervals where the graph of f is concave upward, concave downward and the inflection points.\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Anne<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 #645 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i would do this by calculus...\r<BR>\n" );
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document.write( "dy/dx = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12x%5E2+%2B+72x ALIGN=MIDDLE  ALT=\"-12x%5E2+%2B+72x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0<BR>\n" );
document.write( "so x=0, x=6 are the 2 turning points\r<BR>\n" );
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document.write( "when x=0 then y=-12<BR>\n" );
document.write( "when x=6 then y=420\r<BR>\n" );
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document.write( "d2y/dx2 = -24x + 72\r<BR>\n" );
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document.write( "when x=0, this is positive therefore a MIN<BR>\n" );
document.write( "when x=6, this is negative therefore a MAX\r<BR>\n" );
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document.write( "Ask yourself also the following:\r<BR>\n" );
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document.write( "when x is a HUGE -ve number, what will y be?...here the cube power will dominate, so a cube of a negative number is negative but then there is a negative in front of the cube term too...so y will be hugely postive.\r<BR>\n" );
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document.write( "when x is a HUGE +ve number...the cube will be a huge +ve number then there is the negative sign in front...so y will be hugely negative\r<BR>\n" );
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document.write( "Now armed with this knowledge, sketch the graph, so you can see it and then you can answer where does it increase or decrease...\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-5%2C+12%2C+-50%2C+500%2C+-4x%5E3+%2B+36x%5E2+-+12%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C+12%2C+-50%2C+500%2C+-4x%5E3+%2B+36x%5E2+-+12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "cheers<BR>\n" );
document.write( "Jon. </SPAN>\n" );
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