Question 1072574
v is volume as a function of x; x is the length of corner square to remove.
{{{v=(16-2x)(14-2x)x}}}


Simplify v into general form through multiplications.  Find {{{dv/dx}}}, equate to 0 and look for local maximum.


{{{v=224x-60x^2+4x^3}}}


{{{dv/dx=224-120x+12x^2}}}


Set to 0.

{{{12x^2-120x+224=0}}}
{{{3x^2-30x+56=0}}}
{{{x=(30+- sqrt(228))/(2*3)}}}

{{{x=(30+- 12*sqrt(2))/6}}}


{{{highlight_green(x=5-2*sqrt(2))}}}, x to get maximum v