document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254427>Question 254427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the least value of the polynomial p(x) = x^4 - 4x^3 + 6x^2 - 4x + 6. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186747 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=186747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I couldn't find any formulas that would let you find the minimum of that equation.\r<BR>\n" );
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document.write( "I graphed it instead and saw that the minimum point looks like it is at x = 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-1%2C8%2Cx%5E4+-+4%2Ax%5E3+%2B+6%2Ax%5E2+-+4%2Ax+%2B+6%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-1%2C8%2Cx%5E4+-+4%2Ax%5E3+%2B+6%2Ax%5E2+-+4%2Ax+%2B+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I took 2 points before and after 1 to test this out.\r<BR>\n" );
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document.write( "I chose x = .8 and x = 1.2\r<BR>\n" );
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document.write( "at x = .8, y = 5.0016\r<BR>\n" );
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document.write( "at x = 1.2, y = 5.0016\r<BR>\n" );
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document.write( "this kind of confirms that the axis of symmetry is at x = 1.\r<BR>\n" );
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document.write( "you can try other points like .9 and 1.1, and .7 and 1.3.\r<BR>\n" );
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document.write( "I suspect the minimum point is at x = 1.\r<BR>\n" );
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document.write( "I checked out a website that talked about minimum and maximum points of a polynomial, but I couldn't find anything in there that showed how it could be done other than graphically.\r<BR>\n" );
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document.write( "click here for that.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_poly_maxmin.xml\" target = \"_blank\">http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_poly_maxmin.xml</a>\r<BR>\n" );
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document.write( "at x = 1.2, y =  </SPAN>\n" );
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