document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=949345>Question 949345</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Someone help me with this please. I highly appreciated.\r<BR>\n" );
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document.write( "A function is given. Determine the average rate of change of the function between the given values of the variable.<BR>\n" );
document.write( "f(x) = 5x^2;    x = 4, x = 4 + h </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579612 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=579612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> function is given as f(x) = 5x^2\r<BR>\n" );
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document.write( "you are asked to find the average rate of change when the value of x goes from x = 4 to x = 4+h\r<BR>\n" );
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document.write( "when x = 4, f(4) = 5*4^2 = 5*16 = 80\r<BR>\n" );
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document.write( "when x = 4+h, f(4+h) = 5*(4+h)^2 = 5*(4^2+2*4*h+h^2) = 5*(16+8h+h^2) = 80+40h+5h^2\r<BR>\n" );
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document.write( "you have:<BR>\n" );
document.write( "when x = 4, f(4) = 80<BR>\n" );
document.write( "when x = 4+h, f(4+h) = 80+40h+5h^2\r<BR>\n" );
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document.write( "the rate of change is equal to f(x+h) - f(x) divided by (x+h)-x which simplifies to:\r<BR>\n" );
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document.write( "(f(x+h)-f(x))/h\r<BR>\n" );
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document.write( "when x = 4, this becomes (f(4+h)-f(4)/h\r<BR>\n" );
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document.write( "since f(4+h) = 80+40h+5h^2 and f(4) = 80, this formula becomes:\r<BR>\n" );
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document.write( "(80+40h+h^2-80)/h which becomes:\r<BR>\n" );
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document.write( "(40h+h^2)/h which can be further simplified to:\r<BR>\n" );
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document.write( "40+h\r<BR>\n" );
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document.write( "the average rate of change is equal to 40+h.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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