document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896991>Question 896991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) Find the difference quotient and simplify your answer.<BR>\n" );
document.write( "f(x) = x2 &#8722; x + 8, f(4 + h) &#8722; f(4)/h,  h &#8800; 0\r<BR>\n" );
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document.write( "2) Find the difference quotient and simplify your answer.<BR>\n" );
document.write( "f(x) = 7x2 &#8722; 8x,  f(x + h) &#8722; f(x)/h, h &#8800; 0\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543925 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=543925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -----\r<BR>\n" );
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document.write( "problem number 1:\r<BR>\n" );
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document.write( "f(x) = x2 &#8722; x + 8, f(4 + h) &#8722; f(4)/h, h &#8800; 0\r<BR>\n" );
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document.write( "-----\r<BR>\n" );
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document.write( "f(x) = x^2 - x + 8\r<BR>\n" );
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document.write( "f(4) = 4^2 - 4 + 8 = 16 - 4 + 8 which becomes:\r<BR>\n" );
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document.write( "f(4) = 16 + 4 which becomes:\r<BR>\n" );
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document.write( "f(4) = 20\r<BR>\n" );
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document.write( "f(4 + h) = (4+h)^2 - (4+h) + 8 which becomes:\r<BR>\n" );
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document.write( "f(4 + h) = 16 + 8h + h^2 - 4 - h + 8 which becomes:\r<BR>\n" );
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document.write( "f(4 + h) = h^2 + 7h + 20\r<BR>\n" );
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document.write( "f(4+h) - f(4) = h^2 + 7h + 20 - 20 which becomes:\r<BR>\n" );
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document.write( "f(4+h) - f(4) = h^2 + 7h\r<BR>\n" );
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document.write( "(f(4+h) - f(4)) / h = (h^2 + 7h) / h\r<BR>\n" );
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document.write( "when h is not equal to 0, this can be simplified to:\r<BR>\n" );
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document.write( "(f(4+h) - f(4)) / h = h + 7\r<BR>\n" );
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document.write( "problem number 2:\r<BR>\n" );
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document.write( "f(x) = 7x2 &#8722; 8x, f(x + h) &#8722; f(x)/h, h &#8800; 0 \r<BR>\n" );
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document.write( "-----\r<BR>\n" );
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document.write( "f(x) = 7x^2 - 8x\r<BR>\n" );
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document.write( "f(x+h) = 7(x+h)^2 - 8(x+h) which becomes:\r<BR>\n" );
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document.write( "f(x+h) = 7(x^2 + 2hx + h^2) - 8x - 8h which becomes:\r<BR>\n" );
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document.write( "f(x+h) = 7x^2 + 14hx + 7h^2 - 8x - 8h.\r<BR>\n" );
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document.write( "f(x+h) - f(h) = 7x^2 + 14hx + 7h^2 - 8x - 8h - (7x^2 - 8x) which becomes:\r<BR>\n" );
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document.write( "f(x+h) - f(h) = 7x^2 + 14hx + 7h^2 - 8x - 8h - 7x^2 + 8x which becomes:\r<BR>\n" );
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document.write( "f(x+h) - f(h) = 7h^2 + 14hx - 8h\r<BR>\n" );
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document.write( "the 7x^2 and minus 7x^2 cancel out and the 8x and minus 8x also cancel out.\r<BR>\n" );
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document.write( "(f(x+h) - f(x)) / h = (7h^2 + 14hx - 8h) / h\r<BR>\n" );
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document.write( "when h is not equal to 0, you can simplify this to get:\r<BR>\n" );
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document.write( "(f(x+h) - f(x)) / h = 7h + 14x - 8\r<BR>\n" );
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