A box with a square base and open top must have a volume of 32 cm. We wish to find the dimensions of the box that minimize the amount of material used.
A box with a square base and open top must have a volume of 32 cm^3. We wish to find the dimensions of the box that minimize the amount of material used.
First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base.
Simplify your formula as much as possible.
A(x)=(ans)
Next, find the derivative, A'(x).
A'(x)=(ans)
Now, calculate when the derivative equals zero, that is, when A'(x)=0.
A'(x)=0 when x= (ans)
We next have to make sure that this value of xx gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x).
A"(x)=(ans)
Evaluate A"(x) at the x-value you gave above.
(ans)
can steps be shown neatly please
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
