9 Nov 2021
Problem 12
Page 306
Section 4.6: Optimization Problems
Chapter 4: Applications of Differentiation
Textbook ExpertVerified Tutor
9 Nov 2021
Given information
A box with a square base and open top must have a volume of .
Step-by-step explanation
Step 1.
Let is the length of the sides on the square base and let be the height of the box.
Then the volume of the box is given by
Therefore,
Now, the surface area of the box is
Putting the value of in equation we get:
In other words, our goal is to minimize the function