document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044081>Question 1044081</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The curve for which dy/dx=a(x-p)(x-q) where a,p,q are constants, has turning point at (2,0) and (1,1)\r<BR>\n" );
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document.write( "Determine the value of a using the information above. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659324 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659324\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Turning points of a curve are points where the derivative <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx+=+0 ALIGN=MIDDLE  ALT=\"dy%2Fdx+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "===> the derivative <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=a%28x-p%29%28x-q%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=a%28x-p%29%28x-q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is actually <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+dy%2Fdx=a%28x-2%29%28x-1%29 ALIGN=MIDDLE  ALT=\"+dy%2Fdx=a%28x-2%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "and wouldn't matter whether p=2 and q=1, or p=1 and q=2.\r<BR>\n" );
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document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+dy%2Fdx=a%28x-2%29%28x-1%29+=+a%28x%5E2-3x%2B2%29 ALIGN=MIDDLE  ALT=\"+dy%2Fdx=a%28x-2%29%28x-1%29+=+a%28x%5E2-3x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x%5E3%2F3-3x%5E2%2F2%2B2x%29%2Bc ALIGN=MIDDLE  ALT=\"y+=+a%28x%5E3%2F3-3x%5E2%2F2%2B2x%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after getting the integral.\r<BR>\n" );
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document.write( "Plugging in the respective coordinates of the point (2,0) into the last equation gives \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2a%2F3%2Bc ALIGN=MIDDLE  ALT=\"0+=+2a%2F3%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   (Verify!)\r<BR>\n" );
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document.write( "Similarly, for the point (1,1), we get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+5a%2F6+%2B+c ALIGN=MIDDLE  ALT=\"1+=+5a%2F6+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   (Again verify!)\r<BR>\n" );
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document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a+=+6%29 ALIGN=MIDDLE  ALT=\"highlight%28a+=+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, c = -4, and the curve itself is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x%5E3+-+9x%5E2+%2B+12x+-4 ALIGN=MIDDLE  ALT=\"y+=+2x%5E3+-+9x%5E2+%2B+12x+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " </SPAN>\n" );
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