Question

Verify the Rolle’* Theorem for functions on the indicated intervals: f(x) = cos 2x on [-π/4, π/4]

Answer 1

As we know that cosine function is continuous and differentiable on R.

Let us find the values of the function at an extreme

As we know that cos(-x) = cos x

Here, f'(-π/4) = f(π/4), therefore there exist a c ∈ (-π/4,π/4) such that f'(c) = 0.

Let us find the derivative of f(x)

Here, f'(c) = 0,

Thus, Rolle'* theorem is verified.