Verify Rolles theorem for function `f(x)=cos2(x-pi//4)` on `[0,\ pi//2]` .

Explanation

Since cosine function is continuous and differentiable in `x \in` R


`\therefore f(x) `is continuous in `x \in[0, \pi / 2]-1)` and `f(x)` is differentiable in x \in(0, \pi / 2). Now `{\prime} f(0) =\cos 2(-\pi / 4) =\cos (-\pi / 2) =0 . (\pi / 2) =\cos 2(\frac{\pi}{2}-\frac{\pi}{4}) =\cos \frac{\pi}{2} =0 . \therefore f(0) =f(\pi / 2) . `



`\therefore `Rolle's theorem is applicable.



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