document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194169>Question 1194169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For each of the following expressions, calculate the value of x which gives y a stationary value.<BR>\n" );
document.write( "Determining whether this value of y is a minimum or a maximum. Give your answers correct to 3 significant figures where necessary.<BR>\n" );
document.write( "a) y = x^2 + (2x-1)^2 <BR>\n" );
document.write( "b) y = 2πx - (x-2)^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826341 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=826341\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y=x^2+(2x-1)^2<BR>\n" );
document.write( "y'=2x+2(2x-1)*2=2x+8x-4=10x-4<BR>\n" );
document.write( "set that equal to 0<BR>\n" );
document.write( "10x=4<BR>\n" );
document.write( "x=0.4<BR>\n" );
document.write( "2nd derivative is 10 and is always positive so this is a minimum<BR>\n" );
document.write( "alternative way into expand function to x^2+4x^2-4x+1=5x^2-4x-1<BR>\n" );
document.write( "find vertex by x=-b/2a=-4/-10 or +0.4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C2%2C-10%2C10%2Cx%5E2%2B%282x-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C2%2C-10%2C10%2Cx%5E2%2B%282x-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "y'=2 pi-2(x-2)=2pi-2x+4<BR>\n" );
document.write( "set equal to 0<BR>\n" );
document.write( "2x=2pi+4<BR>\n" );
document.write( "x=2+pi or 5.28<BR>\n" );
document.write( "y''=-2, and this will be a maximum.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C30%2C2%2Api%2Ax-%28x-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C30%2C2%2Api%2Ax-%28x-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );