document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027271>Question 1027271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> [f(x)]^4 = (x + f(x))^3 and f(1)=2.<BR>\n" );
document.write( "What is f'(1)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #642610 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=642610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "I'm going to use y to simplify,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4=x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3 ALIGN=MIDDLE  ALT=\"y%5E4=x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Implicitly differentiating,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E3dy=3x%5E2dx%2B3%28x%5E2dy%2B2xydx%29%2B3%28y%5E2dx%2B2xydy%29%2B3y%5E2dy ALIGN=MIDDLE  ALT=\"4y%5E3dy=3x%5E2dx%2B3%28x%5E2dy%2B2xydx%29%2B3%28y%5E2dx%2B2xydy%29%2B3y%5E2dy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E3dy-3y%5E2dy-3x%5E2dy-6xydy%29=3x%5E2dx%2B6xydx%2B3y%5E2dx ALIGN=MIDDLE  ALT=\"4y%5E3dy-3y%5E2dy-3x%5E2dy-6xydy%29=3x%5E2dx%2B6xydx%2B3y%5E2dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y%5E3-3y%5E2-6xy-3y%5E2%29dy=3%28x%5E2%2B2xy%2By%5E2%29dx ALIGN=MIDDLE  ALT=\"%284y%5E3-3y%5E2-6xy-3y%5E2%29dy=3%28x%5E2%2B2xy%2By%5E2%29dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y%5E3-3y%5E2-6xy-3y%5E2%29dy=3%28x%2By%29%5E2dx ALIGN=MIDDLE  ALT=\"%284y%5E3-3y%5E2-6xy-3y%5E2%29dy=3%28x%2By%29%5E2dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%283%28x%2By%29%5E2%29%2F%284y%5E3-3y%5E2-6xy-3y%5E2%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%283%28x%2By%29%5E2%29%2F%284y%5E3-3y%5E2-6xy-3y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "However, it's not the case that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=2 ALIGN=MIDDLE  ALT=\"f%281%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > because,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%5E4=%281%2B2%29%5E3 ALIGN=MIDDLE  ALT=\"%282%29%5E4=%281%2B2%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=%283%29%5E3 ALIGN=MIDDLE  ALT=\"16=%283%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%3C%3E27 ALIGN=MIDDLE  ALT=\"16%3C%3E27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Actually,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4=%281%2By%29%5E3 ALIGN=MIDDLE  ALT=\"y%5E4=%281%2By%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "has two real solutions,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.55 ALIGN=MIDDLE  ALT=\"y=-0.55\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.63 ALIGN=MIDDLE  ALT=\"y=2.63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which yields two values for the derivatives,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=-0.480 ALIGN=MIDDLE  ALT=\"dy%2Fdx=-0.480\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=1.189 ALIGN=MIDDLE  ALT=\"dy%2Fdx=1.189\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Here is the function along with the two tangent lines at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=gf2.JPG\">.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );