Question 1033573
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An open box is to be made from a 24 in. by 36 in. piece of cardboard by cutting out squares of equal size 
from the four corners and bending up the sides. Find the side of the cut out square so as obtain the maximum volume?
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{{{v=x(24-2x)(36-2x)}}}
{{{v=x(24*36-72x-48x+4x^2)}}}
{{{v=x(24*36-120x+4x^2)}}}
{{{v=4x^3-120x^2+864x}}}



{{{dv/dx=12x^2-240x+864=0}}}
{{{(1/12)(12x^2-240x+864)=0(1/12)}}}
{{{x^2-20x+72=0}}}



{{{D=(20^2-4*72)}}}
{{{D=112}}}
{{{D=4*28}}}



{{{x=(20+- 2*sqrt(28))/2}}} = {{{10 +- sqrt(28)}}}.---------pick what makes sense.


<TABLE> 
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  <TD> 

{{{graph( 330, 330, -2.5, 20.5, -600.5, 1900.5,
          4x^3-120x^2+864x
)}}}


<B>Figure</B>. Function V ={{{4x^3-120x^2+864x}}}

  </TD>
  </TR>
</TABLE>