document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1021879>Question 1021879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using differentiation, estimate how much the function\r<BR>\n" );
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document.write( "f(x)= ax + bln(x)\r<BR>\n" );
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document.write( "increases by, to 2 decimal places, when a = 85 and b = 19, if x increases from 89 to 89.8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #637615 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=637615\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Seems like the hard way to do it.<BR>\n" );
document.write( "Why not just use f(x)?<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdx=a%2Bb%2Fx=85%2B19%2Fx ALIGN=MIDDLE  ALT=\"df%2Fdx=a%2Bb%2Fx=85%2B19%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I'll take the value of the derivative at the average of the two x values,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2889%2B89.8%29%2F2=89.4 ALIGN=MIDDLE  ALT=\"x=%2889%2B89.8%29%2F2=89.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdx=85%2B19%2F89.4=85.212 ALIGN=MIDDLE  ALT=\"df%2Fdx=85%2B19%2F89.4=85.212\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA%2Af=%28df%2Fdx%29%2ADELTA%2Ax ALIGN=MIDDLE  ALT=\"DELTA%2Af=%28df%2Fdx%29%2ADELTA%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA%2Af=%2885.212%29%2889.8-89%29=68.17 ALIGN=MIDDLE  ALT=\"DELTA%2Af=%2885.212%29%2889.8-89%29=68.17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As a comparison,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df=f%2889.8%29-f%2889%29=7650.284-7718.454=68.17002 ALIGN=MIDDLE  ALT=\"df=f%2889.8%29-f%2889%29=7650.284-7718.454=68.17002\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Pretty good approximation\r<BR>\n" );
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