document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=990242>Question 990242</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of x that minimises \r<BR>\n" );
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document.write( "y = 16x^2 + 1800/x\r<BR>\n" );
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document.write( "for positive x. \r<BR>\n" );
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document.write( "So first I need to differentiate, which would give y' = 32x - 1800/x^2\r<BR>\n" );
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document.write( "I am stuck with the next 4 parts..\r<BR>\n" );
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document.write( "How many critical numbers does y have, for positive x?<BR>\n" );
document.write( "Recall that a critical number of a function is a value of x for which the derivative of the function is zero or doesn't exist.\r<BR>\n" );
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document.write( "What is the nature of the critical number of the previous part?<BR>\n" );
document.write( "Enter m for minimum, M for maximum or i for a horizontal point of inflection.\r<BR>\n" );
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document.write( "Give the exact value of the x that minimises y for positive x.<BR>\n" );
document.write( "x (at minimum) =\r<BR>\n" );
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document.write( "Now give the value approximately as a 2 decimal place decimal. Now, give the approximate value (as a 2 decimal place decimal) of the x that minimises y for positive x.<BR>\n" );
document.write( "x (at minimum) &#8776;\r<BR>\n" );
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document.write( "THANK YOU </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #610282 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39631)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=610282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Where is the derivative equal to zero?<BR>\n" );
document.write( "Simplify that derivative and then solve this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=yPrime=32x-1800%2Fx ALIGN=MIDDLE  ALT=\"yPrime=32x-1800%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2832x%29%28x%2Fx%29-1800%2Fx ALIGN=MIDDLE  ALT=\"%2832x%29%28x%2Fx%29-1800%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2832x%5E2-1800%29%2Fx ALIGN=MIDDLE  ALT=\"%2832x%5E2-1800%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2Fx%29%284x%5E2-225%29 ALIGN=MIDDLE  ALT=\"%288%2Fx%29%284x%5E2-225%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The factor of 8 can probably not be needed because you are looking for the NUMERATOR to be zero; and for the same reason, the x in the numerator is not important for this.<BR>\n" );
document.write( "You now just need to solve for  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%284x%5E2-225=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%284x%5E2-225=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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