The answer would be easy to follow!
Ok! look at this. Sin(2x)=2Sin(x)Cos(x). Now subtitute x^2 with U. Now we have the following relation.
f(x)=Sin(U)Cos(U) ==> f(x)=1/2*Sin(2U) ==> f(x)=1/2*Sin(2x^2)
Now since for Sin(U), the first critical point is licated at U=PI/2, we have,
2x^2=PI/2 ==> x=SQRT[PI]/2
That's All. :d