document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1052724>Question 1052724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what type of stationery points does the function y= 12x-3x^2-9 have  and what is the value of y at that point?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #668061 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=668061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The function is y=-3x^2+12x-9<BR>\n" );
document.write( "The derivative is -6x+12<BR>\n" );
document.write( "set that equal to 0<BR>\n" );
document.write( "-6x+12=0<BR>\n" );
document.write( "6x=12<BR>\n" );
document.write( "x=2<BR>\n" );
document.write( "At x=2 the function has a rate of instantaneous change of 0.<BR>\n" );
document.write( "It is positive, so this is a local maximum.<BR>\n" );
document.write( "The value of y is 3<BR>\n" );
document.write( "The vertex x-value is at -b/2a or -12/-6=2 as a check<BR>\n" );
document.write( "f(2)=-12+24-9=3.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );