document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136444>Question 1136444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the slope of the curve at the given point.find the equation of the tangent line at the given point.<BR>\n" );
document.write( "y(3x-y^2)=16 at (4,2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754215 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754215\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the slope of the curve at the given point.find the equation of the tangent line at the given point.<BR>\n" );
document.write( "y(3x-y^2)=16 at (4,2)<BR>\n" );
document.write( "========================<BR>\n" );
document.write( "y(3x-y^2)=16<BR>\n" );
document.write( "y^3 - 3xy = -16<BR>\n" );
document.write( "Differentiate implicitly.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "3y^2*dy - 3x*dy - 3y*dx = 0<BR>\n" );
document.write( "(3y^2* - 3x)*dy = 3y*dx<BR>\n" );
document.write( "(y^2* - x)*dy = y*dx<BR>\n" );
document.write( "dy/dx = y/(y^2 - x)<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "dy/dx = 2/(4 - 4)<BR>\n" );
document.write( "---> infinite slope<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "find the equation of the tangent line at the given point.<BR>\n" );
document.write( "x = 4\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );