document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=608072>Question 608072</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=2-2x^2\r<BR>\n" );
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document.write( "Estimate the intervals on which the function is increasing or decreasing and estimate any relative maxima or minima. Thanks and could you also show work.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #383034 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=383034\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=2-2x^2<BR>\n" );
document.write( "Estimate the intervals on which the function is increasing or decreasing and estimate any relative maxima or minima. Thanks and could you also show work<BR>\n" );
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document.write( "This is a \"quadratic\" because it is a polynomial of degree 2.<BR>\n" );
document.write( "Because it's a quadratic, it is a parabola.<BR>\n" );
document.write( "We know the parabola opens downward because the coefficient associated with the x^2 term is negative (think sad face).<BR>\n" );
document.write( "Since it is a parabola that opens downwards, we know the vertex is at the MAXIMUM.<BR>\n" );
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document.write( "Axis of symmetry:<BR>\n" );
document.write( "x = -b/(2a)<BR>\n" );
document.write( "x = -0/(2(-2))<BR>\n" );
document.write( "x = -0/(-4)<BR>\n" );
document.write( "x = 0<BR>\n" );
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document.write( "Increasing interval:<BR>\n" );
document.write( "(-oo, 0)<BR>\n" );
document.write( "Decreasing interval:<BR>\n" );
document.write( "(0, +oo)<BR>\n" );
document.write( "where oo is for infinity<BR>\n" );
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document.write( "Maximum:<BR>\n" );
document.write( "f(0)=2-2(0)^2<BR>\n" );
document.write( "f(0)=2<BR>\n" );
document.write( "so, max is at (0,2)<BR>\n" );
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