document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992048>Question 992048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this question and provide the workings. Find an equation of the tangent line to the graph of the function f at the point (1, 15). f(x)=&#12310;3x&#12311;^2-11x+23 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611696 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=611696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = 3x^2 -11x + +23<BR>\n" );
document.write( "f'(x) is the first derivative of f(x)<BR>\n" );
document.write( "f'(x) = 6x -11<BR>\n" );
document.write( "f'(x) gives us the slope of the tangent line at any x on f(x)<BR>\n" );
document.write( "we are given the point (1,15), therefore<BR>\n" );
document.write( "slope of tangent line at x = 1 is f'(1) = 6 - 11 = -5<BR>\n" );
document.write( "so far we have<BR>\n" );
document.write( "y = -5x + b<BR>\n" );
document.write( "but we are given the point (1,15)<BR>\n" );
document.write( "15 = -5 + b<BR>\n" );
document.write( "b = 20<BR>\n" );
document.write( "therefore the equation of the line tangent to f(x) at (1,15) is<BR>\n" );
document.write( "y = -5x + 20<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );