Given as the function is f (x) = cos 2x on [0, π]
As we know that cosine function is continuous and differentiable on R. Let us find the values of function at extreme,
⇒ f (0) = cos2(0)
⇒ f (0) = cos(0)
⇒ f (0) = 1
⇒ f (π) = cos2(π)
⇒ f (π) = cos(2 π)
⇒ f (π) = 1
Here, f(0) = f(π), therfore there exist a c belongs to (0, π) such that f’(c) = 0.
Let us find the derivative of f(x)
Hence, Rolle'* theorem is verified.
