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Concept explainers
a.
To write a formula V(x) for the volume of box.
a.
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Answer to Problem 51RE
The required formula is
Explanation of Solution
Given information: A piece of cardboard measures 10 in. by 15 in. Two equal sides are removed from the corners of a 15 in. sides.
Calculation: The required formula is obtained as,
Refer to the diagram exercise 18 of the sction 4.4, but imagine the vertical side as 15” and the horizontal side as 10” .
The length of box be
The width of box be
The height of box be
Hence, the required formula is
b.
To find the domain of V for the problem situation and graph V over this domain.
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 51RE
The domain is: 0 <
Explanation of Solution
Given information: A piece of cardboard measures 10 in. by 15 in. Two equal sides are removed from the corners of a 15 in. sides.
Calculation: The required solution is obtained as,
Hence, the domain is: 0 <
c.
To find the maximum volume and the value of x that gives it, by using a graphical method.
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 51RE
The maximum is at approximately
Explanation of Solution
Given information: A piece of cardboard measures 10 in. by 15 in. Two equal sides are removed from the corners of a 15 in. sides.
Calculation: The required solution is obtained as,
From the graph, the maximum is at approximately
d.
To confirm your result in part (C) analytically.
d.
![Check Mark](/static/check-mark.png)
Answer to Problem 51RE
The required solution is 1.96.
Explanation of Solution
Given information: A piece of cardboard measures 10 in. by 15 in. Two equal sides are removed from the corners of a 15 in. sides.
Calculation: The required solution is obtained as,
Find V’ and where it is = 0.
Hence the required solution is 1.96.
Chapter 5 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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