document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=869495>Question 869495</A>: <I><SPAN STYLE=\"word-break: break-all;\">  	<BR>\n" );
document.write( "The equation of a curve is given by<BR>\n" );
document.write( "y = 6x^5+12<BR>\n" );
document.write( "Obtain the tangent line to the curve at the point where x = 3. Please enter your answer as an equation in the form: y = m x + c<BR>\n" );
document.write( "for some constants m, c. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #524226 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=524226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The slope of the tangent line at x=3 is given by the derivative, dy/dx:<BR>\n" );
document.write( "dy/dx = 30x^4 = 30*3^4 = 2430<BR>\n" );
document.write( "So the line has the form y = 2430x + c<BR>\n" );
document.write( "The value of y at x=3 is given from the original curve:<BR>\n" );
document.write( "y = 6*3^5 + 12 = 1470<BR>\n" );
document.write( "Another point on the line is (0,c)<BR>\n" );
document.write( "So m = (1470-c)/3 = 2430<BR>\n" );
document.write( "c = -2430*3 + 1470 = -5820<BR>\n" );
document.write( "Ans: y = 2430x - 5820 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );