Problem

Problem

A function ff is defined by f(x)=∫0πcos⁡tcos⁡(x−t)dtf(x) = \int_{0}^{\pi} \cos t \cos(x-t) dt , 0≤x≤2π0 \le x \le 2\pi , then which of the following hold(s) good? a. f(x)f(x) is continuous but not differentiable in (0,2π)(0, 2\pi) b. Maximum value of ff is π\pi c. There exists atleast one c∈(0,2π)c \in (0, 2\pi) if f′(c)=0f'(c) = 0 d. Minimum value of ff is −π2-\frac{\pi}{2}

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