document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153277>Question 1153277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me<BR>\n" );
document.write( "If <BR>\n" );
document.write( "f(x) = 6x2 − x3,<BR>\n" );
document.write( " find f '(1) and use it to find an equation of the tangent line to the curve <BR>\n" );
document.write( "y = 6x2 − x3<BR>\n" );
document.write( " at the point (1, 5). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775472 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=775472\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Use \"^\" (shift-6) to denote exponents.<br><BR>\n" );
document.write( "Your function is y = 6x^2-x^3.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+6x%5E2-x%5E3 ALIGN=MIDDLE  ALT=\"y+=+6x%5E2-x%5E3\"   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+=+12x-3x%5E2 ALIGN=MIDDLE  ALT=\"dy%2Fdx+=+12x-3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "At x=1, the derivative (slope) is 12(1)-3(1^2) = 12-3 = 9.<br><BR>\n" );
document.write( "The equation of the tangent line at (1,5) is y = 9x-4.<br><BR>\n" );
document.write( "A graph, showing the function and the tangent line at (1,5):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-15%2C35%2C6x%5E2-x%5E3%2C9x-4%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-15%2C35%2C6x%5E2-x%5E3%2C9x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );