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Q)

The value of $c$ in Rolle's Theorem for the function $f(x)=\cos\large\frac{x}{2}$ on $[\pi,3]$ is

\[\begin{array}{1 1}(1)0&(2)2\pi\\(3)\frac{\pi}{2}&(4)\frac{3\pi}{2} \end{array}\]

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A)
$f(x)= \cos \large\frac{x}{2}$
$f'(x)= -\sin \large\frac{x}{2} \times \frac{1}{2}$
$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.
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