Help me with Calculus

Question

A closed rectangular container with a square base is to have a volume of 2592 in^3. The material for the top and bottom of the container will cost 3 per in^2, and the material for the sides will cost 2 per in^2. Find the dimensions of the container of least cost.

Let x be the length of each edge of the base and y be the height.

Answer 1

x²y = 2,592

y = 2,592/x²

Cost = 3·2·x² + 2·4·xy

C(x) = 6x² + 20,736/x ; x > 0

C^'(x) = 12x - 20,736 / x² = 0

12x³ - 20,736 = 0

x³ = 1728 ; x = 12 ; y = 18