document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=397318>Question 397318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Part of the graph to a curve has equation y=x³-15/2x²+12x-18.\r<BR>\n" );
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document.write( "(a) Find the coordinates of the stationary point E.<BR>\n" );
document.write( "(b) Find the coordinated of G.\r<BR>\n" );
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document.write( "G is on the X axis so Y=0.\r<BR>\n" );
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document.write( "So far I have that <BR>\n" );
document.write( "y=x³-15/2x²+12x-18\r<BR>\n" );
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document.write( "so dy/dx of y=x³-15/2x²+12x-18= 3²-15x+12\r<BR>\n" );
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document.write( "Now, At SP, dy/dx=0<BR>\n" );
document.write( "&#8756; 3x²-15x+12=0<BR>\n" );
document.write( "÷3<BR>\n" );
document.write( "   x²-5x+4=0<BR>\n" );
document.write( "   (x-4)(x-1)=0<BR>\n" );
document.write( "    x=4 or x=1\r<BR>\n" );
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document.write( "Sub x=4 into x³-15/2x²+12x-18      and x=1 into x³-15/2x²+12x-18<BR>\n" );
document.write( "   4³-15/2(4)²+12(4)-18.                1³-15/2(1)+12(1)-18<BR>\n" );
document.write( "   64-120+48-18.                        1-15/2+12-18<BR>\n" );
document.write( "   =-26.                                =-25/2<BR>\n" );
document.write( "   <BR>\n" );
document.write( "    (4,-26).                             (1,-25/2)\r<BR>\n" );
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document.write( "Now I am compltely stuck.<BR>\n" );
document.write( "Can someone please help me.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #281633 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=281633\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "It should be pretty obvious which of the two points is E.  If E is the local maximum as marked on your graph, then the coordinates of E are <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(1,\frac{-25}{2}\right)\">.  Otherwise the coordinates of E are <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (4, -26)\">\r<BR>\n" );
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document.write( "But just to make sure, take the second derivative:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d^2y}{dx^2}\ =\ 6x\ - 15\">\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f^{(2)}(1)\ =\ -9\ <\ 0\">\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(1,\frac{-25}{2}\right)\"> is a local maximum, and \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f^{(2)}(4)\ =\ 9\ >\ 0\">\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (4, -26)\"> is a local minimum.\r<BR>\n" );
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document.write( "If G is on the x-axis, then G is the single real root.  If the x-coordinate of G is a rational number, then the Rational Roots Theorem says that the root must be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \pm1,\pm2,\pm3,\pm6,\pm9\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \pm18\">\r<BR>\n" );
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document.write( "The process is to use synthetic division to test each of the potential rational roots until you find one or have tested them all and concluded that there is no rational root.  In this case there is one, but I'll let you find it for yourself.  If you need a refresher on synthetic division, go to:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"http://www.purplemath.com/modules/synthdiv.htm\">Purple Math - Synthetic Division</a>\r<BR>\n" );
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document.write( "Make sure you read all four pages.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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