Help me, plz!!!!!!

[penny_love]

Yeah!!!! Infinitive is a noun but I agree that infinity is used in maths not infinitive

[Mua Sao Bang]

Uhm, I think I was wrong. Let me check again!

[^^ZhiXiang^^]

well for this one, calculus is the easiest solution.
Figure out the function then just an easy step of Derivative and you'll get it. ^^
May I ask first, the 2nd question asking for the value of what?? is it X?
Either way, to minimize the cost we have to minimize the area of the box, yet keep the same volume.
By the way, in the picture of Dark Angel i'm not agree with the small sides and the big sides he point out, since the base is a square with each side = x, then we will have a base and top with the same area, and the 4 sides have equal area.
For my answer I would say:
I dont have time to draw a picture now but, imagine one rectangular box with square base and top, and 4 sides have the same area.
B= base area = top area, S= side area, x = side of the base, h = height of the box, C = cost
Taken from the info:
C = 2B + 1B + 4S ==> C = 3B + 4S = 3x^2 + 4(x*h).
V = x^2 * h = 324
==> h = 324/x^2
C = 3x^2 + 4(324/x) =======>>>>>>> first answer yay!!!
second answer:
take the derivative of C in term of X.
C' = 6x - 4(324/x^2)
Find x where the 1st derivative = 0
6x - 1296/x^2 = 0
6x^3 - 1296 = 0
x^3 = 1296/6
x^3= 216 =>>> x = 6
use 2nd derivative test we have:
C'' = 6 + 2592/x^3. at x = 6 C''= 6+ 2592/6^3 > 0 (this one is pretty obvious)
============>>>>>>> at x = 6 C is minimum. by 2nd derivative test.
now there is x you can get anything else you want.
Good luck !!! ^^

by XiangXiang

[^^ZhiXiang^^]

Dark Angel: your answer is wrong just because a small mistake ^^, the problem says: square base with a side of x so where did that A come from ^^ The problem is really easy

[Dark Angel]

hehe please read the 7th and 8th post...

and the numbers in the picture were not the answers yet! Thats just a synopsis. Dont be hasty with your answer... take a review carefully

[^^ZhiXiang^^]

oopss sorry, i didnt read those comment. well.
the 2nd answer for the problem, x = 6.
Take a look at the function it's a positive quadratic, so there must be a minimum with X can NOT be 0.
I'm not agree with when X is minimized C is also minimized for all X from 0 to infinity.
mainly because of the part 1296/x.