document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137124>Question 1137124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sketch the graph of the polynomial function f(x)=2x^3-x^2-8x+4. label the zeroes and maximum/mini points. show your work </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754972 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Sketch the graph of the function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E3-x%5E2-8x%2B4 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E3-x%5E2-8x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solution:\r<BR>\n" );
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document.write( "1. Find the relative max and min \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >′=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-2x-8=2%283x%5E2-x-4%29=2%28x+%2B+1%29+%283x+-+4%29 ALIGN=MIDDLE  ALT=\"6x%5E2-2x-8=2%283x%5E2-x-4%29=2%28x+%2B+1%29+%283x+-+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "critical numbers:<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2F3 ALIGN=MIDDLE  ALT=\"x=4%2F3\"   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=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >′′=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-2 ALIGN=MIDDLE  ALT=\"12x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "evaluate at the critical numbers\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >′′<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29=-12-2=-14%3C0 ALIGN=MIDDLE  ALT=\"%28-1%29=-12-2=-14%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>  f concave down\r<BR>\n" );
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document.write( "relative max at <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=2%28-1%29%5E3-%28-1%29%5E2-8%28-1%29%2B4=9 ALIGN=MIDDLE  ALT=\"f%28-1%29=2%28-1%29%5E3-%28-1%29%5E2-8%28-1%29%2B4=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9 ALIGN=MIDDLE  ALT=\"+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is a relative max\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >′′<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29=12%284%2F3%29-2=14+%3E0 ALIGN=MIDDLE  ALT=\"%284%2F3%29=12%284%2F3%29-2=14+%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > f concave up\r<BR>\n" );
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document.write( "relative min at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2F3 ALIGN=MIDDLE  ALT=\"x=4%2F3\"   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=f%284%2F3%29=2%284%2F3%29%5E3-%284%2F3%29%5E2-8%284%2F3%29%2B4=-3.7 ALIGN=MIDDLE  ALT=\"f%284%2F3%29=2%284%2F3%29%5E3-%284%2F3%29%5E2-8%284%2F3%29%2B4=-3.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " =>point:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3.7 ALIGN=MIDDLE  ALT=\"-3.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is a relative min\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C600%2C+-10%2C10%2C+-10%2C+10%2C%0D%0A%0D%0Acircle%284%2F3%2C-3.7%2C.12%29%2Clocate%284%2F3%2C-3.7%2Cmin%284%2F3%2C-3.7%29%29%2C%0D%0Acircle%28-1%2C9%2C.12%29%2Clocate%28-1%2C9%2Cmax%28-1%2C9%29%29%2C%0D%0A%0D%0A+graph%28+600%2C600%2C+-10%2C10%2C+-10%2C+10%2C+2x%5E3-x%5E2-8x%2B4%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );