Check the picture.
let the length of a side of each of the squares removed be x.
The box formed will have dimensions: 80-2x, 50-2x, x(the height)
So the volume can be expressed as a function of x as follows:
f(x)=(80-2x)(50-2x)x=
![[4000-160x-100x+4 x^{2} ]x=(4 x^{2}-260x+4000)x](https://tex.z-dn.net/?f=%5B4000-160x-100x%2B4%20x%5E%7B2%7D%20%5Dx%3D%284%20x%5E%7B2%7D-260x%2B4000%29x)
so

the solutions of f'(x)=0 gives the inflection points, so the candidates for maxima points,

solving the quadratic equation, either by a calculator, graphing software, or by other algebraic methods as the discriminant formula, we find the solutions
x=10 and x=33.333
plug in f(x) these values to see which greater:

cm cubed

which is negative because (50-66.666)<0
Answer: 18000 cm cubed
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I think its figure A but i am not sure.
Answer:
It would roll in this direction.

Step-by-step explanation:
It would roll to the direction of maximum decrease, which is the -1 times the direction of maximum increase, which is given by the gradient of the function.
Since

For this case, the gradient of your function would be

And -1 times the gradient of your function would be

Then, at

So it would go towards

The magnitud of that vector is

and to conclude it would roll in this direction.
