Given the function f(x) defined as:
The change in concavity is given by the inflection points of the function. These points are calculated by the solutions of the equation f''(x) = 0. Then, taking the second derivative of f(x):
Now, the inflection points are:
There is only one inflection point at x = 2. Then, analyzing the concavity for x < 2 and x > 2:
Then, the intervals are: