A function is defined by

MATHEMATICS · Multi correct · CBSE · Mathematics · Integrals · Integrals

Problem

A function

f

is defined by

f(x)=\int_0^\pi\cos t\cos(x-t)\,dt

, where

0\le x\le2\pi

. Which of the following hold good? (1)

f(x)

is continuous but not differentiable in

(0,2\pi)

(2) The maximum value of

f

\pi

(3) There exists at least one

c\in(0,2\pi)

such that

f'(c)=0

(4) The minimum value of

f

-\frac{\pi}{2}