document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044048>Question 1044048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The curve y=ax^3+2x^2+a^2x+b has a minimum point at (-1,0). Find a and b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659284 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39616)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=659284\">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=dy%2Fdx=3ax%5E2%2B4x%2Ba%5E2=0 ALIGN=MIDDLE  ALT=\"dy%2Fdx=3ax%5E2%2B4x%2Ba%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >----Must be for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let x=-1;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a-4%2Ba%5E2=0 ALIGN=MIDDLE  ALT=\"3a-4%2Ba%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, from the derivative being 0 when x is -1;\r<BR>\n" );
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document.write( "ALSO from the original equation,<BR>\n" );
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document.write( "so the problem gives the system of equations,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a%5E2%2B3a-4=0%2Ca%5E2%2Ba-2-b=0%29 ALIGN=MIDDLE  ALT=\"system%28a%5E2%2B3a-4=0%2Ca%5E2%2Ba-2-b=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve this system (first, for \"a\", and then for b).\r<BR>\n" );
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document.write( "First equation of the system is factorable.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-4%29%28a%2B1%29=0 ALIGN=MIDDLE  ALT=\"%28a-4%29%28a%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=-1%2Cor%2Ca=4%29 ALIGN=MIDDLE  ALT=\"system%28a=-1%2Cor%2Ca=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the description gave,  \",... has a minimum point at (-1,0)\".\r<BR>\n" );
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document.write( "Either the equation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%5E3%2B2x%5E2%2Bx%2Bb ALIGN=MIDDLE  ALT=\"y=-x%5E3%2B2x%5E2%2Bx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x%5E3%2B2x%5E2%2B16x%2Bb ALIGN=MIDDLE  ALT=\"y=4x%5E3%2B2x%5E2%2B16x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Do  you believe that the second-derivative might give further information about x at -1 being minimum or maximum?   </SPAN>\n" );
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