document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202117>Question 1202117</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the function f(x)=2x6−12x4.<BR>\n" );
document.write( "The x-intercepts occur at x= \r<BR>\n" );
document.write( "\n" );
document.write( "NOTE: If there are more than one, separate your answers by a comma.\r<BR>\n" );
document.write( "\n" );
document.write( "There a y-intercept at y= \r<BR>\n" );
document.write( "\n" );
document.write( "To analyze the shape of the graph of f it helps to separate the domain into disjoint open intervals<BR>\n" );
document.write( "(−∞,A),(A,B),(B,C),(C,D),(D,E), and (E,∞)<BR>\n" );
document.write( "whose endpoints<BR>\n" );
document.write( "A<B<C<D<E<BR>\n" );
document.write( "are critical points of f or f′. Inside each interval there are no critical points of f or f′, so f′ and f″ cannot change sign inside the interval.\r<BR>\n" );
document.write( "\n" );
document.write( "A= \r<BR>\n" );
document.write( "\n" );
document.write( "B= \r<BR>\n" );
document.write( "\n" );
document.write( "C= \r<BR>\n" );
document.write( "\n" );
document.write( "D= \r<BR>\n" );
document.write( "\n" );
document.write( "E= \r<BR>\n" );
document.write( "\n" );
document.write( "For each of the intervals listed below, select the curve best representing the shape of the graph of f on that interval.\r<BR>\n" );
document.write( "\n" );
document.write( "On (−∞,A): <BR>\n" );
document.write( "?\r<BR>\n" );
document.write( "\n" );
document.write( "On (A,B): <BR>\n" );
document.write( "?\r<BR>\n" );
document.write( "\n" );
document.write( "On (B,C): <BR>\n" );
document.write( "?\r<BR>\n" );
document.write( "\n" );
document.write( "On (C,D): <BR>\n" );
document.write( "?\r<BR>\n" );
document.write( "\n" );
document.write( "On (D,E): <BR>\n" );
document.write( "?\r<BR>\n" );
document.write( "\n" );
document.write( "On (E,∞): <BR>\n" );
document.write( "?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "	 	<BR>\n" );
document.write( "1	 	2<BR>\n" );
document.write( "	 	 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837653 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837653\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=2x^6-12x^4=2x^4(x^2-6)<BR>\n" );
document.write( "x intercepts are where y=0 and  they would be x=0 and x=+/- sqrt(6), so -sqrt(6),0, sqrt(6)<BR>\n" );
document.write( "y intercept at the origin.<BR>\n" );
document.write( "graph is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-3%2C3%2C-64%2C100%2C2x%5E6-12x%5E4%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-3%2C3%2C-64%2C100%2C2x%5E6-12x%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "critical points: get the derivative and set equal to 0.<BR>\n" );
document.write( "So 12x^5-48x^3=0=12x^3(x^2-4)=0, and critical points are at -2,0,2\r<BR>\n" );
document.write( "\n" );
document.write( "The intervals that can be seen are (-oo,-sqrt(6))/// (-sqrt(6),-2)/// (-2,0)/// (0,2)///(2, sqrt(6))///(sqrt(6),oo)<BR>\n" );
document.write( "See if that helps.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );