document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978157>Question 978157</A>: <I><SPAN STYLE=\"word-break: break-all;\"> g(x)= x^4-3x^3+2x^2+x-1.     Find the range.\r<BR>\n" );
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document.write( "I have factored to (x-1)^2(x^2-x-1) and used quadratic equation to find roots of 0.618 and -1.618.  \r<BR>\n" );
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document.write( "What do I need to do from here to find the value of the minimum y value?\r<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 #599628 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=599628\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"Find the range.\"<BR>\n" );
document.write( "g(x) is a polynomial function.  Range will be all real numbers and also domain is all real numbers.\r<BR>\n" );
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document.write( "You could try derivative to help find minimum  (or maximum) y values.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dg%2Fdx=4x%5E3-9x%5E2%2B4x%2B1 ALIGN=MIDDLE  ALT=\"dg%2Fdx=4x%5E3-9x%5E2%2B4x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Where is this equal to 0?   (they may be real, but not rational.)\r<BR>\n" );
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document.write( "There is a MAXIMUM (local) for x=1.  Try then using this root to decompose 4x^3-9x^2+4x+1 into factors. </SPAN>\n" );
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