A function \( f \) is defined by \( f(x)=\int_{0}^{\pi} \cos t \cos...

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A function \( f \) is defined by \( f(x)=\int_{0}^{\pi} \cos t \cos (x-t) d t \)
\( \mathrm{P} \) \( 0 \leq x \leq 2 \pi \), then which of the following hold(s) good?

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(a) \( f(x) \) is continuous but not differentiable in \( (0,2 \pi) \)
(b) Maximum value of \( f \) is \( \pi \)
(c) There exists atleast one \( c \in(0,2 \pi) \) if \( f^{\prime}(c)=0 \)
(d) Minimum value of \( f \) is \( -\frac{\pi}{2} \)
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