document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198146>Question 198146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi!\r<BR>\n" );
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document.write( "A function is given below. Determine the average rate of change of the function between x = 0 and x = 0 + h.<BR>\n" );
document.write( "f(t) = &#8730;-3t \r<BR>\n" );
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document.write( "thanks for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148642 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=148642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "First thing, you have expressed an interval of x = 0 to x = h, but your function is in terms of t.  Either you want f(t) from t = 0 to t = h, or f(x) from x = 0 to x = h -- nothing else makes sense.\r<BR>\n" );
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document.write( "Furthermore, unless <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE h <=0\">, this function is not defined over the reals because the domain of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{x}\"> is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \{x|x\in\R,x\geq 0\}\"> and you have a coefficient of -3 on your independent variable.  But assuming <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE h <=0\"> is the case, let's continue:\r<BR>\n" );
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document.write( "The average rate of change of a function over an interval is the slope of the secant line that passes through the two points on the function at the endpoints of the interval.  So evaluate the function at each endpoint giving you two ordered pairs, in this case <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (0, \sqrt{0})\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (h,\sqrt{-3h})\">.\r<BR>\n" );
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document.write( "The slope of the line passing through two points is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m = \frac{y_1 - y_2}{x_1 - x_2} \">\r<BR>\n" );
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document.write( "so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m = \frac{\sqrt{0} - \sqrt{-3h}}{0 - h} = \frac{\sqrt{-3h}}{h}\">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE h <=0\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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