document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970316>Question 970316</A>: <I><SPAN STYLE=\"word-break: break-all;\"> http://i.imgur.com/OQ38hve.png\r<BR>\n" );
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document.write( "Here is picture if anything came out wrong in copy/paste\r<BR>\n" );
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document.write( "Find the value of x that minimises <BR>\n" );
document.write( "y = 10 x2 +	1900<BR>\n" );
document.write( "x<BR>\n" );
document.write( "for positive x. \r<BR>\n" );
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document.write( "2.1 (1 mark)<BR>\n" );
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document.write( "In order to do that first find the derivative dy/dx.<BR>\n" );
document.write( "dy/dx =  <BR>\n" );
document.write( "Your last answer was: <BR>\n" );
document.write( "20 x&#8722;1900 x&#8722;2\r<BR>\n" );
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document.write( "Your answer is correct.<BR>\n" );
document.write( "The mark for your last attempt was 1.00 <BR>\n" );
document.write( "You previously made one incorrect attempt, and were penalised 0.10, giving an overall mark of 0.90.\r<BR>\n" );
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document.write( "2.2 (1 mark)<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.<BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Your last answer was: <BR>\n" );
document.write( "4.56\r<BR>\n" );
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document.write( "Wrong type <BR>\n" );
document.write( "Your answer should have type <BR>\n" );
document.write( "integer <BR>\n" );
document.write( "but it does not. \r<BR>\n" );
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document.write( "2.3 (1 mark)<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.<BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "You have not attempted this yet \r<BR>\n" );
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document.write( "2.4 (1 mark)<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) =  <BR>\n" );
document.write( "You have not attempted this yet \r<BR>\n" );
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document.write( "2.5 (1 mark)<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;  <BR>\n" );
document.write( "You have not attempted this yet  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592988 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=592988\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2.1) dy/dx = -1900x^(-2) + 20x<BR>\n" );
document.write( "2.2) -1900x^(-2) + 20x = 0<BR>\n" );
document.write( "(20(x^3 - 95)) / x^2 = 0<BR>\n" );
document.write( "for x > 0<BR>\n" );
document.write( "x^3 - 95 = 0<BR>\n" );
document.write( "x = (95)^(1/3)<BR>\n" );
document.write( "answer is 1 solution<BR>\n" );
document.write( "2.3) m (minimum)<BR>\n" );
document.write( "2.4) x = (95)^(1/3) = 4.562902635<BR>\n" );
document.write( "2.5) x(at minimum) = 4.56<BR>\n" );
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