document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116348>Question 1116348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please need assistance\r<BR>\n" );
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document.write( "1) Consider the function f (x) = x square - 4x cube<BR>\n" );
document.write( "(a) Find the stationary points of  .<BR>\n" );
document.write( "(b) Use the First Derivative Test to determine any local maximum or local minimum of  .\r<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 #731283 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=731283\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^2 - 4x^3<BR>\n" );
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document.write( "the first derivative f'(x)<BR>\n" );
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document.write( "f'(x) = 2x -12x^2<BR>\n" );
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document.write( "to find stationary points set f'(x) = 0<BR>\n" );
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document.write( "2x -12x^2 = 0<BR>\n" );
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document.write( "12x^2 -2x = 0<BR>\n" );
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document.write( "x^2 -x/6 = 0<BR>\n" );
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document.write( "complete the square<BR>\n" );
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document.write( "x^2 -x/6 +1/144 = 1/144<BR>\n" );
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document.write( "(x -1/12)^2 = 1/144<BR>\n" );
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document.write( "x -1/12 = sqrt(1/144)<BR>\n" );
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document.write( "x = 1/12 +1/12 = 1/6<BR>\n" );
document.write( "x = 1/12 -1/12 = 0<BR>\n" );
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document.write( "f(1/6) = (1/6)^2 - 4(1/6)^3<BR>\n" );
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document.write( "f(1/6) = (1/36) -4(1/216) = 6/216 -(4/216) = 2/216 = 1/108<BR>\n" );
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document.write( "f(0) = 0^2 -4(0)^3 = 0<BR>\n" );
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document.write( "1.a stationary points are (0,0) and (1/6, 1/108)<BR>\n" );
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document.write( "1.b the second derivative is used to determine local maxima and local minima<BR>\n" );
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document.write( "f''(x) = 2 -24x<BR>\n" );
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document.write( "The sign of the second derivative at the stationary point is positive for a local minimum, and negative for a local maximum. <BR>\n" );
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document.write( "f''(0) = 2 and f''(1/6) = 2 -4 = -2, therefore<BR>\n" );
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document.write( "(0,0) is a local minimum and (1/6, 1/108) is a local maximum<BR>\n" );
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