The correct options are
A monotonically increasing on (−12,0)∪(12,+∞)
D monotonically decreasing on (−∞,−12)∪(0,12)
For calculating increasing or decreasing function, have to calculate f′(x)
f′(x)=4x−1x=0
x=±12 and at x=0 function will not define.
So f′(x)>0 in interval (−12,0)⋃(12,∞), thus in this interval function will monotonically increasing.
f′(x)<0 in interval (−∞,−12)⋃(0,12), thus in this interval function will monotonically decreasing.
Hence, options 'A' and 'D' are correct.