document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=55678>Question 55678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3.      The function f(x)= (x^2+2x)^2/3: (USE CALCULUS to answer a-e)<BR>\n" );
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document.write( ">         a.      Increasing on what interval(s)<BR>\n" );
document.write( ">         b.      Decreasing on what interval(s)<BR>\n" );
document.write( ">         c.      Has critical numbers?<BR>\n" );
document.write( ">         d.      Has Relative Maximum?<BR>\n" );
document.write( ">         e.      Has Relative Minimum?<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 #37783 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=37783\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3. The function f(x)= (x^2+2x)^2/3: (USE CALCULUS to answer a-e)<BR>\n" );
document.write( "f'(x)= (4/3)(x+1)(x^2+2x)^(-1/3)<BR>\n" );
document.write( "> a. Increasing on what interval(s)<BR>\n" );
document.write( "Increasing when f'(x)>0<BR>\n" );
document.write( "f'(x)=0 when x=-1 and f'(x)has a discontinutity at x=-2 and at x=0.<BR>\n" );
document.write( "Need to check the intervals (-inf,-2),(-2,-1),(-1,0),(0,+inf)<BR>\n" );
document.write( "1st interval: if x=-10 f'(-10)= neg/pos <0; f decreasing on (-inf,-2)<BR>\n" );
document.write( "2nd iinterval: if x=(-3/2); f(-3/2)=neg/neg>0; f increasing on (-2,-1)<BR>\n" );
document.write( "3rd interval: if x=-1/2 f'(-1/2)=pos/neg<0; f decreasing on (-1,0)<BR>\n" );
document.write( "4th interval: if x=10 f'(10)=pos/pos: f inceasing on (0,inf)<BR>\n" );
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document.write( "> b. Decreasing on what interval(s)<BR>\n" );
document.write( "See \"a\"<BR>\n" );
document.write( "> c. Has critical numbers?<BR>\n" );
document.write( "x=-2, x=-1, x=0<BR>\n" );
document.write( "> d. Has Relative Maximum?<BR>\n" );
document.write( "x=-1<BR>\n" );
document.write( "> e. Has Relative Minimum?<BR>\n" );
document.write( "At x=-2, x=0<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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