Allouette Shipping Company has a peculiar fee schedule. When determining the pri

Question

Allouette Shipping Company has a peculiar fee schedule. When determining the price to ship a rectangular box, they measure the girth plus the length and multiply the result by $0.65. For a box with a square cross-section (measuring x inches to a side) and costing $260 to ship, the function
V(x) = x^2(400-4x)
gives the volume of the box (in cubic inches).

Find the values of x that are physically possible for such a box (called the relevant domain). Enter your answer as an interval with open parentheses:

Use the first derivative to determine where the function V(x) is decreasing (within the relevant domain). Enter your answer as an interval with open parentheses:

Use the second derivative to determine where the function V(x) is concave up (within the relevant domain). Enter your answer as an interval with open parentheses:

Find the maximum volume we can ship for $260 (having square cross-section).

cubic inches

Explanation / Answer

V[X]= [X^2][400-4X] = 400X^2 - 4X^ 3

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