The question clearly says:
If a function is differentiable and it satisfies f'(-x)=f'(x) then what would be correct.
So, if we could find a function which satisfies the given condition then that should be the answer.
However, in the question , initial condition is met under many functions and almost every function is coming with different answer. So, there must be some problem with the question.
And one more thing as you pointed out "all the options might be true for a specific function, but only 1 (or 2) options would be correct for ALL functions (which satisfy the initial condition)"
ALL Functions includes that specific function as well for which all options are correct!
:)