Question

A rectangular box with a square base has a volume of 4 cubic feet. The material for the bottom of the box costs $3 per square foot, the top costs $2 per square foot, and the four sides cost $5 per square foot.

(a) If x is the side length of the square base, and y is the height of the box, find the total cost of the box as a function of one variable.

(b) Find the critical number of the cost function.

(c) Use the Second Derivative Test to show that the critical number for cost is a local minimum.

Answer #1

A rectangular box with a square base has a volume of 4 cubic
feet. The material for the bottom of the box costs $3 per square
foot, the top costs $2 per square foot, and the four sides cost $5
per square foot Find the critical number of the cost function.

A rectangular box with a square base has a volume of 4 cubic
feet. If x is the side length of the square base, and y is the
height of the box, find the total cost of the box as a function of
one variable The material for the bottom of the box costs $3 per
square foot, the top costs $2 per square foot, and the four sides
cost $5 per square foot. If x is the side length...

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