Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question

Hello, I need help with this question 

You construct an open box from a square piece of material, 36 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure).

 
            
36 − 2x
(a) Write a function V that represents the volume of the box.
V(x) =
 
 


(b) Determine the domain of the function V. (Enter your answer using interval notation.)
 
 


(c) Use a graphing utility to construct a table that shows the box heights x and the corresponding volumes V(x).
x, in V(x), in3
1  
2  
3  
4  
5  
6  
7  

Use the table to estimate a range of dimensions within which the maximum volume is produced.
The x-value is between 1 in and 3 in.The x-value is between 3 in and 5 in.     The x-value is between 5 in and 7 in.

(d) Use the graphing utility to graph V.
   
   

Use the graph to estimate the value of x for which
V(x)
is a maximum. (Round your answer to the nearest whole centimeter.)
x = cm


Compare your result with that of part (c)
The results agree.The results do not agree.    
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