document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205103>Question 1205103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The revenue function for a particular product is R(x)= x(4-0.0001x).How to Find the largest possible revenue.\r<BR>\n" );
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document.write( "to solve this do I just have to find the critical point and check if its the maximum point using the derivative? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841740 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841740\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "The revenue function for a particular product is R(x)= x(4-0.0001x).How to Find the largest possible revenue.<BR>\n" );
document.write( "to solve this do I just have to find the critical point and check if its the maximum point using the derivative?<BR>\n" );
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document.write( "This way of finding critical point of the derivative is one of possible ways to solve\r\n" );
document.write( "the problem, but it assumes that the student knows basic of Calculus.\r\n" );
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document.write( "There are other ways that require knowledge of basics of Algebra, ONLY.\r\n" );
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document.write( "This function  R(x) = x*(4-0.0001x) is a quadratic function, which has x-intercepts at\r\n" );
document.write( "x= 0 and x= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F0.0001 ALIGN=MIDDLE  ALT=\"4%2F0.0001\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 40000.  Hence, it has the maximum half-way between the x-intercepts,\r\n" );
document.write( "which (half-way) is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%2B40000%29%2F2 ALIGN=MIDDLE  ALT=\"%280%2B40000%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40000%2F2 ALIGN=MIDDLE  ALT=\"40000%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20000.\r\n" );
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document.write( "Now, to find the largest possible revenue, simply substitute x= 20000 into the formula for R(x)\r\n" );
document.write( "and get\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29%5Bmax_%5D ALIGN=MIDDLE  ALT=\"R%28x%29%5Bmax_%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20000*(4-0.0001*20000) = 40000.\r\n" );
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document.write( "<U>ANSWER</U>.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29%5Bmax_%5D ALIGN=MIDDLE  ALT=\"R%28x%29%5Bmax_%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 40000.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "There are other simple Algebra ways to solve this problem (and million other similar problems).\r<BR>\n" );
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document.write( "See the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Consider these lessons as your textbook, &nbsp;handbook, &nbsp;tutorials and &nbsp;(free of charge) &nbsp;home teacher.\r<BR>\n" );
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document.write( "Learn the subject from there once and for all.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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