The points of inflection are where the second derivative changes sign. It is the point where the concavity change from upward to downward, or vice versa.
The first derivative is
4(x+3)³
The second derivative is
12(x+3)²
This expression never changes sign. The expression (x+3)⁴ is concave upward everywhere (except x=-3, where it is flat).
There are no points of inflection.
