Let f ( x ) = 2 + cos x for all real x . Statement I For each real t , there exists a point c in [ t , t + π ] such that f ′ ( c ) = 0 . Statement II f ( t ) = f ( t + 2 π ) for each real t .

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f ( x ) = 2 + cos x ∀ x ∈ R Statement I There exists a point c ∈ [ t , t + π ] , where f ′ ( c ) = 0 Hence, Statement 1 is true. Statement II f ( t ) = f ( t + 2 π ) is true. But Statement II is not a correct explanation for Statement I.

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