document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=565992>Question 565992</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Topic : Differentiation\r<BR>\n" );
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document.write( "(Q) The line (l) is the tangent, at the point (2,3), to the curve with equation y = a + bx^2, where a and b are constants. The tangent (l) has gradient 8. Find the values of a and b ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #366078 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=366078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (Q) The line (l) is the tangent, at the point (2,3), to the curve with equation y = a + bx^2, where a and b are constants. The tangent (l) has gradient 8. Find the values of a and b ?<BR>\n" );
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document.write( "The slope (gradient) of the tangent line to the curve y = a + bx^2 is<BR>\n" );
document.write( "dy/dx = 2bx = 2b(2) = 4b<BR>\n" );
document.write( "Since the gradient is 8, we have the value for b:<BR>\n" );
document.write( "4b = 8 -> b = 2<BR>\n" );
document.write( "Now use the equation for the curve to solve for a:<BR>\n" );
document.write( "(x,y) = (2,3)<BR>\n" );
document.write( "3 = a + 2*2^2<BR>\n" );
document.write( "3 = a + 8<BR>\n" );
document.write( "This gives a = -5<BR>\n" );
document.write( "So the curve is y = -5 + 2x^2 </SPAN>\n" );
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