Solution Found!
Maximum Volume You plan to construct an open box with locking tabs from a square piece
Chapter 2, Problem 98(choose chapter or problem)
Maximum Volume You plan to construct an open box with locking tabs from a square piece of material 24 inches on a side by cutting equal squares from the corners and folding along the dashed lines (see figure). (a) Write a function that represents the volume of the box. (b) Determine the domain of the function (c) Sketch a graph of the function and estimate the value of for which is a maximum.
Questions & Answers
QUESTION:
Maximum Volume You plan to construct an open box with locking tabs from a square piece of material 24 inches on a side by cutting equal squares from the corners and folding along the dashed lines (see figure). (a) Write a function that represents the volume of the box. (b) Determine the domain of the function (c) Sketch a graph of the function and estimate the value of for which is a maximum.
ANSWER:Step 1 of 3
An open box with locking tabs is constructed from a square piece of material 24 inches on a side by cutting equal squares from the corners and folding along the dashed lines.
The length of the box is 
Since, the open box is constructed from a square piece of materials, therefore, height of the ox is also 
Thus, the volume of the box is
Hence, the volume of the box can be expressed by the function
