Question 990465
The function V(x) = 2x^3 - 19x^2 + 24x can be factored as:
x(2x-3)(x-8)
Since volume must be greater than zero, the function only makes sense for positive values.
Taking the first factor, we must have x>0, so only positive values of x are allowed.
Also, the product of the other two factors must be greater than 0
The product is positive if both factors are positive, so we must have x-8 > 0 -> x > 8 AND 2x-3 > 0 -> x > 3/2.  
This gives x > 8
The product is also positive if both factors are negative, so we must have x < 8 AND x < 3/2
This gives x < 3/2
So the values for which the function makes sense are
x>0 AND x<3/2 OR x>8