The length of one side, s, of a shipping box is s (x) = ^3√2x, where x is the volume of the box in cubic inches. A manufacturer needs the volume of the box to be between 108 in. 3 and 256 in. 3. What are the minimum and maximum possible lengths of s?

Minimum value: 6 inches,

Maximum value: 8 inches.

Step-by-step explanation:

To find the minimum length of s, we need to use the minimum volume of the shipping box in the equation, so:

s_minimum = ^3√ (2*108) = ^3√216 = 6 inches

The maximum value of the volume will give us the maximum value of the length:

s_maximum = ^3√ (2*256) = ^3√512 = 8 inches

So the minimum value of the length is 6 inches and the maximum value is 8 inches.