document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131288>Question 1131288</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the intermediate value theorem, determine, if possible, whether the function f has at least one real zero between a and b. f(x)=x^(3)+4x^(2)-6x-13; a=-8, b=-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747915 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=747915\">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%5E%283%29%2B4x%5E%282%29-6x-13 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E%283%29%2B4x%5E%282%29-6x-13\"   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=a=-8 ALIGN=MIDDLE  ALT=\"a=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-4+ ALIGN=MIDDLE  ALT=\"b=-4+\"   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%28-8%29=%28-8%29%5E%283%29%2B4%28-8%29%5E%282%29-6%28-8%29-13 ALIGN=MIDDLE  ALT=\"f%28-8%29=%28-8%29%5E%283%29%2B4%28-8%29%5E%282%29-6%28-8%29-13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-8%29=-221 ALIGN=MIDDLE  ALT=\"f%28-8%29=-221\"   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%28-4%29=%28-4%29%5E%283%29%2B4%28-4%29%5E%282%29-6%28-4%29-13 ALIGN=MIDDLE  ALT=\"f%28-4%29=%28-4%29%5E%283%29%2B4%28-4%29%5E%282%29-6%28-4%29-13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-4%29=11 ALIGN=MIDDLE  ALT=\"f%28-4%29=11\"   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=-221 ALIGN=MIDDLE  ALT=\"x=-221\"   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=11 ALIGN=MIDDLE  ALT=\"x=11\"   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 continuous, so somewhere in between the curve must cross through <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0 ALIGN=MIDDLE  ALT=\"f%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Yes, there is a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%283%29%2B4x%5E%282%29-6x-13=+0 ALIGN=MIDDLE  ALT=\"x%5E%283%29%2B4x%5E%282%29-6x-13=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the interval [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   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=+graph%28+600%2C+600%2C+-15%2C+15%2C+-10%2C10%2C+x%5E%283%29%2B4x%5E%282%29-6x-13%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-15%2C+15%2C+-10%2C10%2C+x%5E%283%29%2B4x%5E%282%29-6x-13%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
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