document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854501>Question 854501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle has one corner on the graph of y=36-x^2 another at the origin a 3rd on the positive y-axis, and the fourth on the positive x-axis. Express the area A of the rectangle as a function of x. What is the domain of A? For what value of x is A largest?<BR>\n" );
document.write( "ANY HELP WOULD BE SOOOO WELCOME!! Thanks in advance I am super confused! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514742 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=514742\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It's a good 1st step to draw the parabola<BR>\n" );
document.write( "and also a horizontal line which represents<BR>\n" );
document.write( "both the point on the y-axis ( 0, y ) and<BR>\n" );
document.write( "also the intersection of this line with the <BR>\n" );
document.write( "parabola ( x, y ).<BR>\n" );
document.write( "Remember that the horizontal line can be<BR>\n" );
document.write( "ANY horizontal line<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+40%2C+24%2C+-x%5E2+%2B+36+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+40%2C+24%2C+-x%5E2+%2B+36+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So far,  I have the points:<BR>\n" );
document.write( "( 0, 0 )<BR>\n" );
document.write( "( 0, y )<BR>\n" );
document.write( "( x, y )<BR>\n" );
document.write( "Now I can add the final point ( x1, 0 )<BR>\n" );
document.write( "Both x and y are positive<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+x%2Ay+ ALIGN=MIDDLE  ALT=\"+A+=+x%2Ay+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+x%2A%28+-x%5E2+%2B+36+%29+ ALIGN=MIDDLE  ALT=\"+A+=+x%2A%28+-x%5E2+%2B+36+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-x%5E3+%2B+36x+ ALIGN=MIDDLE  ALT=\"+A+=+-x%5E3+%2B+36x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can plot this on top of the previous plot<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+100%2C+18%2C+-x%5E2+%2B+36%2C+-x%5E3+%2B+36x+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The domain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+ ALIGN=MIDDLE  ALT=\"+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Are you in a calculus class? That's the only way I know to <BR>\n" );
document.write( "find the peak of 3rd degree equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-x%5E3+%2B+36x+ ALIGN=MIDDLE  ALT=\"+A+=+-x%5E3+%2B+36x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%27+=+-3x%5E2+%2B+36+ ALIGN=MIDDLE  ALT=\"+A%27+=+-3x%5E2+%2B+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%27+=+0+ ALIGN=MIDDLE  ALT=\"+A%27+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( slope = 0 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3x%5E2+%2B+36+=+0+ ALIGN=MIDDLE  ALT=\"+-3x%5E2+%2B+36+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%5E2+=+36+ ALIGN=MIDDLE  ALT=\"+3x%5E2+=+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+=+12+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+2%2Asqrt%283%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+2%2Asqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > for which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is largest<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "and now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+-x%5E2+%2B+36+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+-x%5E2+%2B+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+-%28+2%2Asqrt%283%29+%29%5E2+%2B+36+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+-%28+2%2Asqrt%283%29+%29%5E2+%2B+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+-4%2A3+%2B+36+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+-4%2A3+%2B+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+36+-+12+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+36+-+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+24+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Hope this all makes sense- if you do it with a<BR>\n" );
document.write( "non-calculus method, you should get the<BR>\n" );
document.write( "same answer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );