# Math Help - The toughest minimization problem I have ever done...

1. ## The toughest minimization problem I have ever done...

I have attached a copy of the problem I need help with. It is task #5. This problem is part of a larger problem dealing with the surface area of a cylinder. I have been able to solve the previous four tasks. Here are all the important formulas and values that I have so far:

h= 1000/((pi)r^2)

In task 4, found the values for r and h that I think may be helpful in task 5:

r = 250^(1/3)/3^(1/6)
h= [1000*3^(2/6)]/[250^(2/3)*(pi)

h/r is given in the problem in task #4.

I am having a difficult time knowing where and how to begin. I believe that we must find k, but I don't know if I have done that right. Also, assuming that we find a numerical value for k, do we need to include that into the equation or do we treat the variable as a constant? Either way, I can't seem to properly differentiate the first equation. Please help!

2. Originally Posted by bandito1989
I have attached a copy of the problem I need help with. It is task #5. This problem is part of a larger problem dealing with the surface area of a cylinder. I have been able to solve the previous four tasks. Here are all the important formulas and values that I have so far:

h= 1000/((pi)r^2)

In task 4, found the values for r and h that I think may be helpful in task 5:

r = 250^(1/3)/3^(1/6)
h= [1000*3^(2/6)]/[250^(2/3)*(pi)

h/r is given in the problem in task #4.

I am having a difficult time knowing where and how to begin. I believe that we must find k, but I don't know if I have done that right. Also, assuming that we find a numerical value for k, do we need to include that into the equation or do we treat the variable as a constant? Either way, I can't seem to properly differentiate the first equation. Please help!
This looks like and investigation that is part of your assessment.

I am closing this thread and will reopen it only if you can provide a convincing argument that it is not part of your final assessment.

CB