document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997829>Question 997829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x) = 2x^2 - 9x Find all extreme values (if any) of f on the interval [0, 9]\r<BR>\n" );
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document.write( "So far I have:<BR>\n" );
document.write( "f'(x) = 4x - 9 <BR>\n" );
document.write( "f(x) = x = 4/9<BR>\n" );
document.write( "If I plug back into the original function I can find either the max or min value.\r<BR>\n" );
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document.write( "f(4/9) = 2(4/9)^2 - 9(4/9) = - 10.125 (calculator) <BR>\n" );
document.write( "However, how do I know whether this is the max or min value without a graphical refrence?\r<BR>\n" );
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document.write( "Also, isn't there a rule with extrema stating that since the interval notation is [0,9] that I can use the 9? if so why not the 0. This rule keeps tripping me up.\r<BR>\n" );
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document.write( "Please explain<BR>\n" );
document.write( "Thank you<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615756 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So far I have:<BR>\n" );
document.write( "f'(x) = 4x - 9<BR>\n" );
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document.write( "At the min or max, f'(x) = 0<BR>\n" );
document.write( "4x-9 = 0<BR>\n" );
document.write( "x = 9/4<BR>\n" );
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document.write( "f(9/4) = 2*81/16 - 9*9/4<BR>\n" );
document.write( "= 81/8<BR>\n" );
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document.write( "It's a parabola in x.  The x^2 term is positive --> opens upward<BR>\n" );
document.write( "--> a minimum.<BR>\n" );
document.write( "The 1st derivative is linear --> 1 extreme.<BR>\n" );
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document.write( "f(x) = x = 4/9<BR>\n" );
document.write( "If I plug back into the original function I can find either the max or min value.\r<BR>\n" );
document.write( "\n" );
document.write( "f(4/9) = 2(4/9)^2 - 9(4/9) = - 10.125 (calculator) <BR>\n" );
document.write( "However, how do I know whether this is the max or min value without a graphical refrence?\r<BR>\n" );
document.write( "\n" );
document.write( "Also, isn't there a rule with extrema stating that since the interval notation is [0,9] that I can use the 9? if so why not the 0. This rule keeps tripping me up.<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "9/8 is between 0 and 9, so that's not an issue.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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