$f(x)= \cos \large\frac{x}{2}$
$f'(x)= -\sin \large\frac{x}{2} \times \frac{1}{2}$
$f'(c) =\large\frac{1}{2} $$ \sin \large\frac{c}{2}$
$f'(c)=0 => \large\frac{1}{2} $$- \sin \large\frac{c}{2} $$=0$
=> $ \sin \large\frac{c}{2}=0$
$\large\frac{c}{2} $$=0$
$c=0$
Hence 1 is the correct answer.