document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887420>Question 887420</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the tangent line to y=3x^2+0.6x-3 at x=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 #536606 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=536606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the tangent line to y=3x^2+0.6x-3 at x=1.5<BR>\n" );
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document.write( "y-value when x=1.5<BR>\n" );
document.write( "y=3x^2+0.6x-3<BR>\n" );
document.write( "y=3(1.5)^2+0.6(1.5)-3<BR>\n" );
document.write( "y=6.75+0.9-3<BR>\n" );
document.write( "y=4.65<BR>\n" );
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document.write( "Now, you have a point at (1.5, 4.65)<BR>\n" );
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document.write( "Next find the first derivative:<BR>\n" );
document.write( "y' = 6x + 0.6<BR>\n" );
document.write( "slope at x=1.5 is<BR>\n" );
document.write( "6(1.5) + 0.6<BR>\n" );
document.write( "9.6 (slope)<BR>\n" );
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document.write( "Now, using the slope (9.6) and the single point (1.5, 4.65) plug into \"point-slope\" form:<BR>\n" );
document.write( "y - y1 = m(x - x1)<BR>\n" );
document.write( "y - 4.65 = 9.6(x - 1.5)<BR>\n" );
document.write( "y - 4.65 = 9.6x - 14.4<BR>\n" );
document.write( "y = 9.6x - 9.75 (equation of line in \"slope-intercept\" form)<BR>\n" );
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