I've tried this many times but can't seem to get the correct answer

Question

For the function V(x)= (36-2x)(36-2x)(x), 0<x<18

 

Use a graphing utility to create a table that shows box heights x, the width,  and the corresponding volumes V.

 

HEIGHT               WIDTH           VOLUME

1                            x                     V

2                            x                     V  

3                            x                     V

4                            x                     V

5                            x                     V

6                            x                     V

7                            x                     V

 

 

Use the table to estimate the dimensions that will produce a maximum volume.(in inches)

 

lenth=

 

width= 

height= 

Answer 1

The formula for volume a box is length times width times height.  The variable x represents height.  The other factors in the formula represent the length and width.  These factors are the same.

 

length = 36 - 2x = width

 

From what I can see, your table has mixed up labeling according to the statement above it.  The height column should be labeled 1 to 17.  The width column should be labeled (36 - 2x) all the way down.

 

Evaluate V(x)  in the interval   0 < x < 18     to get your width and volume.  I will do the first one for you so you understand what I mean.

 

 

V(x)  at  x=1

 

V(1) = (36 - 2x)(36 - 2x)(x)

        = (36 - 2)(36 - 2)(1)

        = 34 * 34 * 1

        = 1156

 

This means that at height of 1, the width is 34 and volume is 1156.

 

 

Do this process 16 more times to get the width and volume.

 

 

To find the dimensions that produce the maximum volume, look for the volume at the point in which V(x) changes from increase to decrease.