document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202652>Question 1202652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given f(x) = x^2 +3, find and simplify the difference quotient ([f(x+h) - f(x)])/h.\r<BR>\n" );
document.write( "\n" );
document.write( "What is the best way to go about solving this? I know I need to substitute the equations together like (x+h)^2 + 3 - (x^2=3)\r<BR>\n" );
document.write( "\n" );
document.write( "I don't know if that substitution is correct. Any help with this problem would be greatly appreciated.<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837601 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=837601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe it works like this.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you want the limit of (f(x + h) - f(x)) / h as h approaches 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation if f(x) = x^2 + 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(x+h) is derived by replacing x with (x + h) in the original equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(x+h) = (x+h)^2 + 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify this to get f(x+h) = x^2 + 2hx + h^2 + 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(f(x + h) - f(x)) / h becomes (x^2 + 2hx + h^2 + 3 - (x^2 + 3)) / h which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x^2 + 2hx + h^2 + 3 - x^2 - 3) / h\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2hx + h^2 / h\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h from the numerator and the denominator cancel out and you are left with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x + h\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "as h approaches 0, this becomes 2x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your derivative.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the results from the derivative calculator at <a  rel=nofollow HREF= \"https://www.derivative-calculator.net/\" target = \"_blank\">https://www.derivative-calculator.net/</a> confirm that the derivative is 2x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the derivative is the same as the limit of [f(x+h) - f(x)] / h, as h approaches 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let me know if you still have any questions regarding this.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "theo\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );