blushelk322Lv1
20 Nov 2021
Problem 10f
Page 306
Section 4.6: Optimization Problems
Chapter 4: Applications of Differentiation
Textbook ExpertVerified Tutor
20 Nov 2021
Given information
Consider the following scenario: A box with an open top is to be made from a 3 ft wide square piece of cardboard by cutting a square from each of the four corners and bending up the edges. Determine the maximum volume that such a box can have. Obtain an equation that relates the variables of volume.
To determine and compare the answer.
Step-by-step explanation
Step 1.
A square piece of cardboard 3 ft-wide, by cutting out a square from each corner.
The volume (V) of the box is:
The length of the box is given as: 3 ft
The side of the box is constructed from the original square piece.
This means that:
So