document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978149>Question 978149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the equation for the tangent line at point(1,0) in the curve y=3x²-4x+1 is, y= ? and the area surrounded by the curve the tangen line ans the y-axis is?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #599652 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=599652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation for the tangent line at point(1,0) in the curve y=3x²-4x+1 is, y= ? <BR>\n" );
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document.write( "y' = 6x - 4 = the slope, m<BR>\n" );
document.write( "m = 2<BR>\n" );
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document.write( "y = 2(x - 1)<BR>\n" );
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document.write( "and the area surrounded by the curve the tangen line ans the y-axis is?<BR>\n" );
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document.write( "Find the x-ints of the parabola, the zeroes:<BR>\n" );
document.write( "3x^2 - 4x + 1 = 0<BR>\n" );
document.write( "(3x-1)*(x-1) = 0<BR>\n" );
document.write( "x = 1/3, x = 1<BR>\n" );
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document.write( "The bounded area is the triangle below the x-axis.<BR>\n" );
document.write( "Its area = 1 sq unit.<BR>\n" );
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document.write( "Add the area under the parabola from x = 0 to x = 1/3 is:<BR>\n" );
document.write( "f(x) = 3x^2 - 4x + 1<BR>\n" );
document.write( "INT = x^3 - 2x^2 + x  (ignore the constant)<BR>\n" );
document.write( "Area = INT(1/3) - INT(0)<BR>\n" );
document.write( "= 1/27 - 2/9 + 1/3 - 0<BR>\n" );
document.write( "= 4/27 sq units<BR>\n" );
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document.write( "The area from 1/3 to 1 has to be subtracted:<BR>\n" );
document.write( "Area = INT(1) - INT(1/3)<BR>\n" );
document.write( "= [1/27 - 2/9 + 1/3] - (1 - 2 + 1)<BR>\n" );
document.write( "= 4/27<BR>\n" );
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document.write( "Total area = 1 sq unit<BR>\n" );
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document.write( "I think the other tutor got the area for the parabola, the tangent and the x-axis.  Not the y-axis.<BR>\n" );
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