Maximum Volume of Folded Box: Proving and Solving Using Differentiation

[Mmx]

Sorry my maths question is in Malay ill try to translate as gd as i can. I realyl have no idead how to do it.

A zink which have a square size of 30 cm x 16 cm.
At the end of the 4 edge of the sqaure zink is cut out equally same sides x cm.

After cutting the zink is fold into a a open box.

a) Prove that the volume, V of this box is equal to V=4(x^3 - 23x^2 + 120x)cm^3

b) After that, find the maksimum volume, V

If you can understand then nvm cause my maths are in malay and not english. In malay this topic are call Pembezaan I am not sure in english that is call differences. I can understand better with the look of working. Sorry

 

[VietDao29]

Sorry my maths question is in Malay ill try to translate as gd as i can. I realyl have no idead how to do it.

A zink which have a square size of 30 cm x 16 cm.
At the end of the 4 edge of the sqaure zink is cut out equally same sides x cm.

After cutting the zink is fold into a a open box.

a) Prove that the volume, V of this box is equal to V=4(x^3 - 23x^2 + 120x)cm^3

b) After that, find the maksimum volume, V

If you can understand then nvm cause my maths are in malay and not english. In malay this topic are call Pembezaan I am not sure in english that is call differences. I can understand better with the look of working. Sorry

Okay, I think I understand what you mean...
Do you know the formula for computing the volume of a box: $$\mbox{V = length x height x depth} = \mbox{A_{base}} \mbox{ x height}$$?
So after you fold that zink into an open box, what's the length, the depth, and the height of that box?
So, your zink will look like this:
__|¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯|__
|...........|
|...........|
|...........|
|...........|
¯¯|_______________|¯¯
Hint, the base is the rectangle in red. Can you find its area?
Can you find the height of the box?
From there, can you find its volume?
--------------
For number 2, do you know how to differentiate?
For example f(x) := x³ + x
=> f'(x) = 3x² + 1.
Can you do this?
If yes, then do you know how one can find an maximum value and minimum value of a function by differentiation?

 

[Mmx]

Thx. Yes i know how to differentiate that's y my malay call Pembezaan. Thx for the hint. I Can do it now.