A container manufacturer plans to make rectangular boxes whose bottom and top measure 3x by 4x. The container must contain 48 cm^3. The top and the bottom will cost $3.50 per square centimeter, while the four sides will cost $4.40 per square centimeter.
What should the height of the container be so as to minimize cost? Round your answer to the nearest hundredth.

The height of the container that minimize cost is 3.08 cm

Step-by-step explanation:

Let

h ---> the height of the container

we know that

The volume of the box is equal to

substitute

The function cost is equal to

To find out the minimum cost determine the first derivative

equate to zero

Find the height of the container

substitute the value of x

cheater

step-by-step explanation: