Question #6d4ae

1 Answer
Oct 23, 2016

Answer:

#2/3 " inch"#

Explanation:

Let the size of square to be cut from each corner #=x " inch"#
Volume of the open box so formed #V=lxxwxxh=(8-2 x)xx(3-2x)xx x#
#=>V=(24-22 x+4x^2)xx x#
#=>V=24x-22 x^2+4x^3#
To find maximum value we need to differentiate #V# with respect to #x# and equate it to #0#
#(dV)/dx=d/dx(24x-22 x^2+4x^3)#, setting it equal to zero we get
#24-44 x+12x^2=0#, dividing both sides by #4# and rearranging we get
#3x^2-11x+6=0#
Using split the middle term method to find the roots of above we get
#3x^2-9x-2x+6=0#
#=>3x(x-3)-2(x-3)=0#
#=>(x-3)(3x-2)=0#
We get the roots as
#x=3, 2/3#

For #x=3#, we see that width #w# of the box becomes negative. Hence, ignoring this root we have size of the square #2/3 " inch"#