Finding the global minimum.

[Rumor]

At least, I think that's what this question is asking for.

"The total cost to build an open box with a constant volume V and with a square base is given by the function

C(x)=10x^2+(60V/x)

where x is the length of the square base.

a) Find the value of x that will produce the box with the minimum total cost. Your answer will involve the parameter of V.

b) Verify that this value of x will give the local minimum.

c) Give an argument based on calculus why this value of x actually gives a global minimum, not just a local minimum."

I'm not sure how to do this.
Any help, please?

 

[Deleted member 4993]

At least, I think that's what this question is asking for.

"The total cost to build an open box with a constant volume V and with a square base is given by the function

C(x)=10x^2+(60V/x)

where x is the length of the square base.

a) Find the value of x that will produce the box with the minimum total cost. Your answer will involve the parameter of V.

b) Verify that this value of x will give the local minimum.

c) Give an argument based on calculus why this value of x actually gives a global minimum, not just a local minimum."

I'm not sure how to do this.
Any help, please?

The cost function has one variable - x.

What are the conditions for local/global extrema for this function?

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.