document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1067685>Question 1067685</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I need to find and simplify the difference quotient for f(9 + h)- f(9), over h. Where f(x) = x^2 &#8722; x + 8. h cannot = 0.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #682877 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=682877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We wish to find [f(x+h) - f(x)]/h, for h very small, and x = 9<BR>\n" );
document.write( "Substituting the values in the function we get [(x+h)^2 - (x+h) + 8 - (x^2 - x + 8)]/h<BR>\n" );
document.write( "Expand and simplify:<BR>\n" );
document.write( "[(x^2 + 2xh + h^2 - x - h + 8 - x^2 + x - 8]/h <BR>\n" );
document.write( "We see that all the x^2 and constant terms drop out and we are left with <BR>\n" );
document.write( "[2xh + h^2 - h]/h -> h + 2x - 1<BR>\n" );
document.write( "Substituting x = 9 gives h + 18 - 1. For h very small, this reduces to 17.<BR>\n" );
document.write( "Ans: 17 </SPAN>\n" );
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