Let \( f'(x) = \dfrac{192x^3}{(2+\sin^4(n\pi))} \) for all \( x \in \Re \) with \( f\left(\dfrac{1}{2}\right) = 0 \). If \( m \le \int _{ \frac{1}{2} }^{ 1 }{ f(x)dx } \le M \), then the possible values of \( m \) and \( M \) are
1
\( m= 13 ,M = 24 \)
2
\( m= \dfrac{1}{4} ,M = \dfrac{1}{2} \)
3
\( m= -11 ,M = 0 \)
4
\( m= 1,M =12\)