document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993477>Question 993477</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 I know I need to differentiate, but I am not sure where to go from there?\r<BR>\n" );
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document.write( "32x - (1800/x^2)\r<BR>\n" );
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document.write( "I need:\r<BR>\n" );
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document.write( "How many critical numbers does y have, for positive x?\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 #612759 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=612759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = 16x^2 + 1800/x <BR>\n" );
document.write( "dy/dx = 32x -(1800/x^2)<BR>\n" );
document.write( "to find min x for positive x set dy/dx = 0<BR>\n" );
document.write( "32x -(1800/x^2) = 0<BR>\n" );
document.write( "multiply both sides of = by x^2<BR>\n" );
document.write( "32x^3 - 1800 = 0<BR>\n" );
document.write( "32x^3 = 1800<BR>\n" );
document.write( "x = (15/2)^(2/3)<BR>\n" );
document.write( "for positive x, x is a local minimum<BR>\n" );
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document.write( "x(at minimum) = (15/2)^(2/3)<BR>\n" );
document.write( "x(at minimum) = 3.831547162 approx 3.83<BR>\n" );
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document.write( "here is the graph of y = 16x^2 + 1800/x to help visualize this problem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+5%2C+-4000%2C+4000%2C+%2816%2Ax%5E2%29+%2B+1800%2Fx%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-5%2C+5%2C+-4000%2C+4000%2C+%2816%2Ax%5E2%29+%2B+1800%2Fx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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