document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993814>Question 993814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the interval(s) where the function f(x)=x^3-4x+2 is decreasing. For me to better understand this problem I think I would benefit from understanding the method behind solving this equation and all the information related to solving of this problem. I appreciate all your help and would greatly appreciate a -step-by-step system for solving to fully understand this porblem and other similar porblems. 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 #612998 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=612998\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we use the first derivative of f(x) = x^3 -4x +2<BR>\n" );
document.write( "I assume f(x) is continuous on an interval I and differentiable on the interior of I, then if first derivative is < 0 for all x belonging to I, then f(x) is decreasing on I<BR>\n" );
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document.write( "first derivative of f(x) = x^3 -4x +2 is<BR>\n" );
document.write( "f'(x) = 3x^2 - 4<BR>\n" );
document.write( "therefore f(x) is decreasing on the open interval (-4/3, 4/3)<BR>\n" );
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document.write( "here is the graph of f(x) = x^3 -4x +2 to help visualize the solution<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-3%2C+3%2C+-10%2C+15%2C+x%5E3+-4%2Ax+%2B2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-3%2C+3%2C+-10%2C+15%2C+x%5E3+-4%2Ax+%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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