
#1
Aug2708, 07:14 PM

P: 341

1. The problem statement, all variables and given/known data
Find the dimensions of a rectangular box with the largest volume with surface area 64cm^2. 2. Relevant equations area of a rectangular prism 2xy+2yz+2xz 3. The attempt at a solution took 2xy+2yz+2xz=64 rearranging for z: z=(xy32)/(y+x) partial derivative of z with respect to x y/(y+x)(xy32)/(y+x)^2 partial derivative of z with respect to y x/(y+x) (xy32)/(y+x)^2 setting both derivatives equal to zero to obtain the critical point.... Here's where I hit a wall I cannot get a real root for y. y/(y+x)(xy32)/(y+x)^2 y^2+xy=xy32 y^2=32 Please only help me up to this point until I ask you to help me further, I want to challenge myself. Thank you! 



#2
Aug2708, 07:27 PM

P: 2,258

what are you maximizing?




#3
Aug2708, 07:32 PM

P: 341

The volume of this box.




#4
Aug2708, 07:38 PM

P: 2,258

Dimensions of box with largest volume
you're maximizing xyz?




#5
Aug2708, 07:45 PM

P: 341

Oh wait I'm finding the maximum dimensions that can be used to get the surface area of 64cm^2. So I maximize 2xy+2yz+2xz=64




#6
Aug2708, 08:01 PM

P: 2,258

'maximum dimensions'?




#7
Aug2708, 08:06 PM

P: 341

The problem states that I must find the dimensions of a rectangular box with the largest volume if it's total surface area is 64cm^2. What we don't know is how long those dimensions are.




#8
Aug2708, 08:19 PM

P: 2,258

first you should find the maximum volume of a box with surface area 64cm^2.




#9
Aug2708, 08:22 PM

P: 341

Okay! I'll take the problem from there and tell you how I made out.



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