You are now 25 years old and hope to save $600,000 for retirement at age 65. You are very unsure about the outlook for investment returns. If you assume no earnings on your investments, how much will you have to save each year?
15,000
10,000
5,000
11,111

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume (), in cubic centimeters, and surface area (), in square centimeters, of the box with a square base are described below:

(1)

(2)

Where:

- Side length of the base, in centimeters.

- Height of the box, in centimeters.

By (2), we clear within the formula:

And we apply in (1) and simplify the resulting expression:

(3)

Then, we find the first and second derivatives of this expression:

(4)

(5)

If and , then we find the critical value of the side length of the base is:

Then, we evaluate this result in the expression of the second derivative:

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

The largest possible volume of the box is 2000000 cubic meters.