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Discuss the applicability for Rolle’s theorem, when:

f(x) = cos 1/x on [-1, 1]

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Best answer

Condition (1):

Since, f(x) = cos 1/x which is discontinuous at x = 0

⇒ f(x) = cos 1/x is not continuous on [-1,1].

Condition (1) of Rolle’s theorem is not satisfied.

So, Rolle’s theorem is not applicable.

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