document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126649>Question 1126649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box is formed by cutting squares from the four corners of a 9\"-wide by 12\"-long sheet of paper and folding up the sides. <BR>\n" );
document.write( "Let x represent the length of the side of the square cutout (in inches), and let V<BR>\n" );
document.write( "represent the volume of the box (in cubic inches).<BR>\n" );
document.write( "A)Write a formula that expresses V in terms of x.<BR>\n" );
document.write( "B)Suppose the function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Write a function formula for F.<BR>\n" );
document.write( "C)What is the domain of f? Enter your answer as an interval<BR>\n" );
document.write( "D)What is the range of f? Enter your answer as an interval<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #742972 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=742972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is V=(9-2x)(12-2x)*x<BR>\n" );
document.write( "f(x)=4x^3-42x^2+108x<BR>\n" );
document.write( "x domain is (0, 4.5) units inches, because x=0 has no volume and x=4.5 has no volume either.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C6%2C-10%2C100%2C4x%5E3-42x%5E2%2B108x%2C%289-2x%29%2812-2x%29%2Ax%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the range requires the maximum<BR>\n" );
document.write( "derivative is 12x^2-84x+108<BR>\n" );
document.write( "divide by 12 and set equal to 0<BR>\n" );
document.write( "x^2-7x+9=0<BR>\n" );
document.write( "x=(1/2)(7+/-sqrt(13)), and only sensible root is 1.70<BR>\n" );
document.write( "f(1.70)=81.872 in^3\r<BR>\n" );
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document.write( "Range is (0, 81.87), units in^3. </SPAN>\n" );
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