Question

A rectangular box has length x and width 3. The volume of the box is given by y = 3x(8 – x). The greatest x-intercept of the graph of this polynomial equals which of the following? Choose all that apply. The maximum possible width. The maximum possible length. The minimum possible height. The maximum possible height. The maximum possible volume.

Answer 1

7 this is because x=7=4 which is 11+9 which is 20

Answer 2

Option B and C

Explanation:

Given : A rectangular box has length x and width 3. The volume of the box is given by
`y = 3x(8-x)`

To find : The greatest x-intercept of the graph of this polynomial equals which of the following?

Consider rectangular box with volume
`y = 3x(8-x)`

Where,

Length x units (x≥0); (given)

Width 3 units; (given)

Comparing with the formula of volume

`V=length* width* height`

Height (8-x) units i.e, 8-x≥0, then x≤8

The volume of the rectangular box presented as,

`V=x* 3* 8-x`

Maximal possible of height can be 8 units (x=0) and minimal possible height can be 0 (x=8)

We can see from the attached graph,

That the greatest x-intercept is x=8, then the height will be minimal and length will be maximal.

Then the volume will be V=0 (minimal).

Therefore, the correct answer are B (the maximum possible length), C (the minimum possible height).