document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=990405>Question 990405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A function H is differentiable at x =4. An equation for the line tangent to the graph of H at x=4 is 2x + 3y = 5. Find H(4) and H'(4). \r<BR>\n" );
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document.write( "Please explain this. <BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #610486 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=610486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x + 3y = 5<BR>\n" );
document.write( "solve for y<BR>\n" );
document.write( "3y = -2x + 5<BR>\n" );
document.write( "y = -2x/3 + 5/3<BR>\n" );
document.write( "y = -2x/3 + 5/3<BR>\n" );
document.write( "when x = 4<BR>\n" );
document.write( "y = -2(4)/3 + 5/3 = -1<BR>\n" );
document.write( "therefore we have a point of H(x) which is (4, -1)<BR>\n" );
document.write( "H(4) = -1<BR>\n" );
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document.write( "H'(x) is the slope of the tangent to H(x). It passes through (4, -1): that is the point at which it is tangent.<BR>\n" );
document.write( "Remember that the equation of the tangent is<BR>\n" );
document.write( "y = -2x/3 + 5/3<BR>\n" );
document.write( "So the slope of the tangent line is -2/3. And it is H’(4), therefore<BR>\n" );
document.write( "H'(4) = -2/3\r<BR>\n" );
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