Question

the volume of a rectangular cardboard box is modeled by the functions v(x)=(18-2x)(3-2x)x where x is the width

Answer 1

The given function of volume v(x)=(18-2x)(3-2x)x is true for certain boundaries of x which is mentioned below.

Explanation:

The equation for the volume is represented as:

v(x)=(18-2x)(3-2x)x

• As x represents the width, it cannot be negative or zero. X must be greater than 0.
• For the equation (18-2x), the term can't be negative or zero so,

18-2x > 0

or, 2x < 18

or, x < 9

• For the term, 3-2x > 0

or, 2x < 3

or, x < 1.5

This develops the boundary for x as,

0 < x < 1.5