We don't know f (x) but we do know that x = 1 is a critical number of f' (x) and we know f" (x)=12x. use this information to decide if f(x) has a relative minimum or maximum at x=1.

relative minimum

Step-by-step explanation:

From f^''(x) = 12x we can take the integration to find out what f'(x) is:

Furthermore, we can substitute x = 1 for f''(x) to find out whether it's positive or negative

f''(1) = 12*1 = 12 > 0

So if x=1 is a critical point of f'(x) and f''(x=1) > 0 then that point is a relative minimum point