document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163278>Question 1163278</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The level of water in a rain gutter is given by the following<BR>\n" );
document.write( "V(t) =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10t+sqrt%28+4-t%5E2+%29+ ALIGN=MIDDLE  ALT=\"+10t+sqrt%28+4-t%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note : The square root contains 4-t^2\r<BR>\n" );
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document.write( "a. Determine dV/dt\r<BR>\n" );
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document.write( "b. Is the water level rising or falling at t = 1.5 seconds?\r<BR>\n" );
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document.write( "Thank you.\r<BR>\n" );
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document.write( "10t(√4-t^2)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #787330 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=787330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Use the product rule and the chain rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ V(t)\ =\ 10t\sqrt{4\,-\,t^2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dV}{dt}\ =\ 5t\(4\,-\,t^2\)^{-\frac{1}{2}}\(-2t\)\ +\ 10\(4\,-\,t^2\)^{\frac{1}{2}}\">\r<BR>\n" );
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document.write( "Evaluate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{dV}{dt}\|_{t=1.5}\">\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{dV}{dt}\|_{t=1.5}\ >\ 0\"> then rising\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{dV}{dt}\|_{t=1.5}\ <\ 0\"> then falling\r<BR>\n" );
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document.write( "And, of course, if it is equal to zero it is doing neither, it is either at a minimum or a maximum.<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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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