Differentiation question help. *question attached below*

Question

itiaax · Answer

Can someone walk me through this question please? I have no idea where to start :O

itiaax · Answer

attachment

itiaax · Answer

How do we show this?

itiaax · Answer

Yes, it is a bit confusing. How did the values 1152 and 768 come in?

itiaax · Answer

Is it that we ought to rearrange the volume formula in terms of x and y?

zepdrix · Answer

Oh my bad, I skipped part a),
they wanted us to show something didn't they >.<

itiaax · Answer

Yes!

zepdrix · Answer

$$\Large\rm V=xyz$$$$\Large\rm 384=xyz$$$$\Large\rm \color{orangered}{\frac{384}{z}=xy}$$
Mmm yah I assume we're doing something with this.

zepdrix · Answer

So we need to add up all of the area that was used to make this box.
It becomes a tad tricky because of the divider in the middle.

zepdrix · Answer

We have `three` of the yz pieces,
and `one` of the xy pieces (because it's an OPEN box),
and `two` of the xz pieces of wood.

This make sense?

zepdrix · Answer

$$\Large\rm A=3yz+xy+2xz$$

zepdrix · Answer

From there we can use our volume information (our constraint) to get our `Area Function` in terms of x and y! :)

itiaax · Answer

How do we know how much yz and xy and xz pieces we have? :o

zepdrix · Answer

|dw:1413070946946:dw|The area of this front panel is xz, yes?