The dimensions of a rectangular prism are length = (x -1), width = (x - 5), and height = (x - 7). Find the approximate relative maximum value for the volume of the rectangular prism.

Select one:
a. 14.2
b. 16.9
c. 18.5
d. 10.3

Question

The dimensions of a rectangular prism are length  = (x -1), width = (x - 5), and height =  (x - 7).  Find the approximate relative maximum value for the volume of the rectangular prism.

Select one:
a. 14.2
b. 16.9
c. 18.5
d. 10.3

1645323 · Answer

@ganeshie8 @phi

phi · Answer

You should complain to your teacher about this question.

They want you to either use calculus or plot the curve and look for a local maximum
If we plot the curve we get the attached graph.

*However*,  notice the local maximum occurs at approximately x= 2.57
this means the dimensions of your prism  will have negative values.  
Example, width = (x - 5) = -2.43  which is clearly bogus.

They should just ask, what is the local maximum for the cubic curve defined by y= (x-1)(x-5)(x-7)
when they introduce the idea that these are the dimensions of a prism they went off the tracks  (and should not be allowed to make up math questions)