document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=280076>Question 280076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=8x-3x^2 i must indicate if it has a maximum or minimum. how do i go about this </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #203557 by </B><A HREF=/tutors/aboutme.mpl?userid=dabanfield><B>dabanfield(803)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dabanfield><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=203557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=8x-3x^2 i must indicate if it has a maximum or minimum. how do i go about this<BR>\n" );
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document.write( "We need to find the \"critical points\" by taking the first derivative of f and setting that equal to zero:\r<BR>\n" );
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document.write( "f'(x) = 8 - 6x <BR>\n" );
document.write( "8 - 6x = 0<BR>\n" );
document.write( "x = 4/3\r<BR>\n" );
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document.write( "So a max or min occurs at x = 4/3.\r<BR>\n" );
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document.write( "The second derivative test tells us if we have a max or min:\r<BR>\n" );
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document.write( "f''(x) = -6\r<BR>\n" );
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document.write( "Since f''(x) < 0 for all x including x = 4/3 we know x = 4/3 is where a maxiumm occurs. The actual value of the maximum is:\r<BR>\n" );
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document.write( "f(4/3) = 8*(4/3) - 3*(4/3)^2 </SPAN>\n" );
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