Final answer:
The function is concave up in its entire domain and the point of inflection occurs at x = 1.
Step-by-step explanation:
The function is given by f(x) = 2 / (x-1)^4. To discuss the concavity and the point for this function, we need to find the second derivative and determine its sign. Let's start by finding the first and second derivatives:
f'(x) = -8 / (x-1)^5
f''(x) = 40 / (x-1)^6
Since the second derivative is always positive for any x > 1, the function is concave up in its entire domain. The point of inflection occurs at x = 1.