Given as the function is f(x) = sin3x on [0, π]
As we know that sine function is continuous and differentiable on R. Let us find the values of function at extreme,
⇒ f (0) = sin3(0)
⇒ f (0) = sin0
⇒ f (0) = 0
⇒ f (π) = sin3(π)
⇒ f (π) = sin(3 π)
⇒ f (π) = 0
Here, f(0) = f(π), therefore there exist a c belongs to (0, π) such that f’(c) = 0.
Let us find the derivative of f(x)
Thus, Rolle'* theorem is verified.
