Question #6d4ae

1 Answer
A08
Oct 23, 2016

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"

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