document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224339>Question 224339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Me and my friend are trying to do this problem but have no clue how to do it.\r<BR>\n" );
document.write( "\n" );
document.write( "Here's the problem:\r<BR>\n" );
document.write( "\n" );
document.write( "Use the Intermediate Value Theorem to show that there is a root of the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E3+%2B+x%5E2+%2B+2+=+0+ ALIGN=MIDDLE  ALT=\"+2x%5E3+%2B+x%5E2+%2B+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the interval [-2,-1]\r<BR>\n" );
document.write( "\n" );
document.write( "We have a very vague understanding of what that theorem means but we only worked with letters never an actual equation. Could you please help us? Thanks 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 #167700 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=167700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the Intermediate Value Theorem to show that there is a root of the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E3+%2B+x%5E2+%2B+2+=+0+ ALIGN=MIDDLE  ALT=\"+2x%5E3+%2B+x%5E2+%2B+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the interval [-2,-1]<BR>\n" );
document.write( ".<BR>\n" );
document.write( "f(x) = 2x^3 + x^2 + 2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Calculate f(-2):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E3+%2B+x%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"+2x%5E3+%2B+x%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28-2%29%5E3+%2B+2%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"+2%28-2%29%5E3+%2B+2%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28-8%29+%2B+4+%2B+2 ALIGN=MIDDLE  ALT=\"+2%28-8%29+%2B+4+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-16+%2B+4+%2B+2 ALIGN=MIDDLE  ALT=\"+-16+%2B+4+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-10+ ALIGN=MIDDLE  ALT=\"+-10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Calculate f(-1):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E3+%2B+x%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"+2x%5E3+%2B+x%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28-1%29%5E3+%2B+%28-1%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"+2%28-1%29%5E3+%2B+%28-1%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28-1%29+%2B+1+%2B+2 ALIGN=MIDDLE  ALT=\"+2%28-1%29+%2B+1+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2+%2B+1+%2B+2 ALIGN=MIDDLE  ALT=\"+-2+%2B+1+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1 ALIGN=MIDDLE  ALT=\"+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "\"Mean value theorem\" says that if a number (say 0) is between f(-2)=-10 and f(-1)=1 then there will be a value of x that will give you that result.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since 0 lies between -10 and 1 there is a value of x.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "To find that value, it is best to use a graphing calculator..<BR>\n" );
document.write( "x = -1.197<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Read up more on \"intermediate value theorem\" at:<BR>\n" );
document.write( "http://en.wikipedia.org/wiki/Intermediate_value_theorem<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );