document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970034>Question 970034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here is another one..I am stumped as to what to do!! Help please!! I need steps to understand this.\r<BR>\n" );
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document.write( "Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.<BR>\n" );
document.write( "f(x)=x^5-x^4+5x^3-4x^2-20x+18: [1.5,1.9]\r<BR>\n" );
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document.write( "Thank you in advance!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592716 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=592716\">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=f%28x%29=x%5E5-x%5E4%2B5x%5E3-4x%5E2-20x%2B18 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E5-x%5E4%2B5x%5E3-4x%5E2-20x%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" >:  interval:[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.9 ALIGN=MIDDLE  ALT=\"1.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >] \r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.5 ALIGN=MIDDLE  ALT=\"x=1.5\"   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%281.5%29=%281.5%29%5E5-%281.5%29%5E4%2B5%281.5%29%5E3-4%281.5%29%5E2-20%281.5%29%2B18 ALIGN=MIDDLE  ALT=\"f%281.5%29=%281.5%29%5E5-%281.5%29%5E4%2B5%281.5%29%5E3-4%281.5%29%5E2-20%281.5%29%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281.5%29=-1.59375 ALIGN=MIDDLE  ALT=\"f%281.5%29=-1.59375\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.9 ALIGN=MIDDLE  ALT=\"x=1.9\"   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%281.9%29=%281.9%29%5E5-%281.9%29%5E4%2B5%281.9%29%5E3-4%281.9%29%5E2-20%281.9%29%2B18 ALIGN=MIDDLE  ALT=\"f%281.9%29=%281.9%29%5E5-%281.9%29%5E4%2B5%281.9%29%5E3-4%281.9%29%5E2-20%281.9%29%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281.9%29=11.58389 ALIGN=MIDDLE  ALT=\"f%281.9%29=11.58389\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we know:\r<BR>\n" );
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document.write( "    at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.5 ALIGN=MIDDLE  ALT=\"x=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the curve is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=below ALIGN=MIDDLE  ALT=\"below\"   DISABLED_style= \"max-width:90%; height:auto;\" > zero<BR>\n" );
document.write( "    at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.9 ALIGN=MIDDLE  ALT=\"x=1.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the curve is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=above ALIGN=MIDDLE  ALT=\"above\"   DISABLED_style= \"max-width:90%; height:auto;\" > zero\r<BR>\n" );
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document.write( "And, being a polynomial, the curve will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=continuous ALIGN=MIDDLE  ALT=\"continuous\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So, somewhere in between, the curve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=must ALIGN=MIDDLE  ALT=\"must\"   DISABLED_style= \"max-width:90%; height:auto;\" > cross through <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   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=drawing%28+600%2C+600%2C+-5%2C+5%2C+-15%2C+15%2C+%0D%0Acircle%281.5%2C0%2C.08%29%2Ccircle%281.9%2C0%2C.08%29%2Ccircle%281.59204%2C0%2C.08%29%2C%0D%0Alocate%281.59204%2C0.8%2Cp%281.59204%2C0%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+10%2C+x%5E5-x%5E4%2B5x%5E3-4x%5E2-20x%2B18%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "zero is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.59204 ALIGN=MIDDLE  ALT=\"x=1.59204\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%3C1.59204%3C1.9 ALIGN=MIDDLE  ALT=\"1.5%3C1.59204%3C1.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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