The correct option is C (0,4a)
f(x)=x√4ax−x2
Differentiate w.r.t ′x′
f1(x)=xα√4ax−x2×(4a−2x)+√4ax−x2
=x(4a−2x)α√4ax−x2+√4ax−x2
=xα(2x−a)α√4ax−x2+√4ax−x2
=(2x−a)x√4ax−x2+√4ax−x2
Equatef1(x)=0
0=(2x−a)x√4ax−x2+√4ax−x2
−√4ax−x2=(2x−a)x√4ax−x2
−(√4ax−x2)2=(2x−a)x
4ax−x2=2ax−x2
2ax=0
x=0
So factor is x√x(4a−x)=0
x=0or√x(4a−x)=0
4ax−x2=0
x2=4ax
x=4a
SInce the function has the range (0,4a)
(0,4a) falls in this range