Verify the Rolle’* Theorem for functions on the indicated intervals: f(x) = (6x/π) - 4sin^2 x on [0,π/6]

Question 1

Verify the Rolle’* Theorem for functions on the indicated intervals: f(x) = (6x/π) - 4sin2 x on [0,π/6]

Question 2

As we know that the sine functions are continuous and differentiable on R.

Let us find the values of the function f at an extreme

Here, f(0) = f(π/6), therefore there exist a c ∈ (0,π/6) such that f'(c) = 0.

Let us find the derivative of f(x)

Since, f'(c) = 0

Thus, Rolle'* theorem is verified.

kratos · Answer 1 · 2020-05-30T23:21:00+0000

As we know that the sine functions are continuous and differentiable on R.

Let us find the values of the function f at an extreme

Here, f(0) = f(π/6), therefore there exist a c ∈ (0,π/6) such that f'(c) = 0.

Let us find the derivative of f(x)

Since, f'(c) = 0

Thus, Rolle'* theorem is verified.

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