document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001594>Question 1001594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please check my answers:\r<BR>\n" );
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document.write( "Q: Let f(x) = 2x^3 - 3x^2 + 6. Find the max and min values of f on [-1,1]\r<BR>\n" );
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document.write( "A: f'(x) = 6x^2 - 6x<BR>\n" );
document.write( "= 6x(x - 1) =0<BR>\n" );
document.write( "x=0, x=+1 critical values. However, +1 is already there so 2nd der test is not needed.\r<BR>\n" );
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document.write( "f\"(x) = 12x-6<BR>\n" );
document.write( "f\"(0) = 12(0)-6=-6<0, therefore a MIN occurs at 0.\r<BR>\n" );
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document.write( "plugging in the x-values given.<BR>\n" );
document.write( "f(1) = 2(1)^3-3(1)^2+6 = 5<BR>\n" );
document.write( "f(-1) = 2(-1)^3-3(-1)^2+6 = 1\r<BR>\n" );
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document.write( "After graphing it looks like (-1,7) is the MIN and (0,6) is the MAX.\r<BR>\n" );
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document.write( "Is this correct?\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 #618722 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=618722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2nd Derivative Test: if f '' (x) is negative on some interval, then the region on f(x) is concave DOWN (not up). So we have a max on this interval. That means a local max is at x = 0.\r<BR>\n" );
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document.write( "I think you meant to say (-1,1) instead of (-1,7)\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "Local Max = (0,6)<BR>\n" );
document.write( "Local Min = none<BR>\n" );
document.write( "Absolute Max = (0,6) <BR>\n" );
document.write( "Absolute Min = (-1,1) </SPAN>\n" );
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