To compare: the x -intercept and the maximum of the function and then interpret the significance of the results.
Box 2 has a greater maximum value, so it has a greater volume.
The volume of box 2 decreases less with the increasing side length of a cut square.
Given information:
The cardboard for box 1 is 8 inches by 3 inches and the cardboard for box 2 is 6 inches by 4 inches. The volume of box 1 is
Concept Used:
The area of the rectangle is calculated by
Calculation:
First calculate the area of first box then area of the second box.
Both boxes have same area.
The graph of the second box is shown below:
From the above graph, it is observed that the maximum volume is
The graph of the first box is shown below:
From the above graph, it is observed that the maximum volume is
Since
The x -intercept of box 1 is 0 and 1.5 and the x -intercept of box 2 is 0 and 2, so the volume of the second box decreases less with increasing side lengths of a cut square.
Chapter 5 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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