The coordinates of the inflection point in the problem you presented is not just one point because there is no given f(x). We can integrate f'(x) to get f(x) but we still don't know what arbitrary constant C is.
f'(x) = 6x2 + 6x - 252
Integrate both sides of the equation:
f(x) = 2x3 +3x2 - 252x + C
In Differential Equation, f(x) and the inflection points can be graph using slope fields and we can leave C as it is. Therefore your question can be answered with C in it.
If we are looking for the inflection point, f''(x) = 0
f''(x) = 12x +6 = 0
x =-1/2
f(-1/2) = 2(-1/2)3 + 3(-1/2)2 - 252 (-1/2) + C
f(-1/2) = 253/2 + C
Therefore the inflection point is (-1/2, 253/2 +C).
