JEE Advanced 2007 Mathematics question

Mathematics Application of Derivatives JEE Advanced 2007

Let f(x) = 2 + cos x for all real x. STATEMENT-1 : For each real t, there exists a point c in [t, t + π] such that f′(c) = 0. because STATEMENT-2 : f(t) = f(t + 2π) for each real t.

(A)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1Correct
(C)Statement-1 is True, Statement-2 is False
(D)Statement-1 is False, Statement-2 is True

Answer: (B)

Solution

at x = kπ. Every closed interval of length π, [t, t + π], contains a multiple of π, so Statement-1 is true. Statement-2: cos x has

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Question ID VK-037525