Respuesta :
There are points on the interval [π, 5π] where f is not continuous and there are points on the interval (π, 5π) where f is not differentiable.
What is Rolle's theorem?
Rolle's theorem, sometimes known as Rolle's lemma, states that any real-valued differentiable function that reaches equal values at two independent places must have at least one stationary point in between, i.e. a point where the first derivative is zero.
As we know, the condition for the Rolle's theorem is:
- f(a) = f(b)
- f(x) must be continuous in [a, b]
- f(x) must be differentiable in (a, b)
The function is:
f(x) = cotx/2
The cot function is not continuous at x = nπ, n ≠ 0
The cot functions are not differentiable at x = nπ, n ≠ 0
Thus, there are points on the interval [π, 5π] where f is not continuous and there are points on the interval (π, 5π) where f is not differentiable.
Learn more about the Rolle's theorem here:
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