Square Sheet of Cardboard Problem

[pataflora]

The question and the answer choices are in the screenshots. Need it asap if possible please.

 

[Dr.Peterson]

What help do you need? Please show what you have tried, so we can see where you are stuck, and what we can assume you know.

We don't just do the work for you, as you know from reading https://www.freemathhelp.com/forum/threads/complete-posting-guidelines-from-the-sites-owner.109846/. (You did read that, right?)

 

[pataflora]

Alright so I got the equation to look like this in terms of x since L = 20-2x, W = 10-x, H= x
V = 2x^3 - 40x^2 +200x

 

[pataflora]

Then the derivative of that is
V ' = 6x^2 - 80x + 200

 

[pataflora]

The value of x that makes V’ = 0 is 10 and 10/3

 

[pataflora]

What I am stuck in is if that would be a maximum volume, minimum volume, or both

 

[Dr.Peterson]

What have you been taught about determining whether a critical value is a min or a max? Have you tried checking the second derivative, or looking at the signs of the first derivative?

One thing you might do is to sketch a graph of your function; take particular note of what happens at x=10, as well as end behavior.

 

[pataflora]

Yeah, I see that when x = 10, it will give a result of 0 when substituted back in the original equation. However, when x = 10/3, its gives the value of about 296.

 

[pataflora]

So x = 10 cannot be possible while x = 10/3 gives a maximum volume?

 

[Dr.Peterson]

In a sense, x=10 gives a minimum volume (0), but then it isn't really a box at all!

So, yes, x = 10/3 gives the maximum volume.

That's why D is the best choice; but if they allowed more than one choice, I might also select A.

 

[lev888]

Yeah, I see that when x = 10, it will give a result of 0 when substituted back in the original equation. However, when x = 10/3, its gives the value of about 296.

Yes. Or just look at the 20x20 sheet and imagine what would happen to it if we cut off 4 10" squares.

 

[pataflora]

Ok, thanks for the clarifications. Thank you all so much.