document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163395>Question 163395</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618317821/algebrahomeworkh>Algebra and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> given: f(x)=5x-x^2<BR>\n" );
document.write( "find: f(5-h)-f(5)/h </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120379 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=120379\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given: f(x)=5x-x^2<BR>\n" );
document.write( "find: f(5-h)-f(5)/h<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "f(x) = 5*x - x^2<BR>\n" );
document.write( "f(5-h) is gotten by replacing x with (5-h), so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285-h%29+=+5%2A%285-h%29+-+%285-h%29%5E2 ALIGN=MIDDLE  ALT=\"f%285-h%29+=+5%2A%285-h%29+-+%285-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "f(5) is gotten by replacing x with 5, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29+=+5%2A5+-+%285%29%5E2 ALIGN=MIDDLE  ALT=\"f%285%29+=+5%2A5+-+%285%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since there is no parentheses around it, your formula f(5-h)-f(5)/h<BR>\n" );
document.write( "is assumed to be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285-h%29+-+%28f%285%29%2Fh%29 ALIGN=MIDDLE  ALT=\"f%285-h%29+-+%28f%285%29%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if you meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%285-h%29+-+f%285%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28f%285-h%29+-+f%285%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >, that would be a different equation.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "i'll solve for<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285-h%29+-+%28f%285%29%2Fh%29 ALIGN=MIDDLE  ALT=\"f%285-h%29+-+%28f%285%29%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285-h%29+-+%28f%285%29%2Fh%29+=+5%2A%285-h%29+-+%285-h%29%5E2+-+%28%285%2A5+-+%285%29%5E2%29%2Fh%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+-+5%2Ah+-+%2825-10%2Ah+%2B+h%5E2%29+-+%28%2825-25%29%2Fh%29 ALIGN=MIDDLE  ALT=\"25+-+5%2Ah+-+%2825-10%2Ah+%2B+h%5E2%29+-+%28%2825-25%29%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+-+5%2Ah+-+25+%2B+10%2Ah+-+h%5E2+-+%280%2Fh%29 ALIGN=MIDDLE  ALT=\"25+-+5%2Ah+-+25+%2B+10%2Ah+-+h%5E2+-+%280%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ah+-+h%5E2 ALIGN=MIDDLE  ALT=\"5%2Ah+-+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "as far as i can tell.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if you really meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%285-h%29+-+f%285%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28f%285-h%29+-+f%285%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the equation becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A%285-h%29+-+%285-h%29%5E2+-+%285%2A5+-+%285%29%5E2%29%29%2Fh ALIGN=MIDDLE  ALT=\"%285%2A%285-h%29+-+%285-h%29%5E2+-+%285%2A5+-+%285%29%5E2%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825+-+5%2Ah+-+25+%2B+10%2Ah+-+h%5E2+-+25+%2B+25%29%2Fh ALIGN=MIDDLE  ALT=\"%2825+-+5%2Ah+-+25+%2B+10%2Ah+-+h%5E2+-+25+%2B+25%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2Ah+-+h%5E2%29+%2F+h ALIGN=MIDDLE  ALT=\"%285%2Ah+-+h%5E2%29+%2F+h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+-+h ALIGN=MIDDLE  ALT=\"5+-+h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "either way the key is to substitute (5-h) for x in f(5-h), and to substitute (5) for x in f(5)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );