JEE Main 2012 Mathematics question

Consider the function f(x) = |x − 2| + |x − 5|, x ∈ R. Statement 1: f′(4) = 0 Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5).

(1)Statement 1 is false, statement 2 is true
(2)Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1Correct
(3)Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
(4)Statement 1 is true, statement 2 is false

Answer: (2)

Solution

On [2, 5], f(x) = (x − 2) + (5 − x) = 3, a constant, so f′(4) = 0 — Statement 1 true. Statement 2 is true (f(2) = f(5) = 3, f continuous and

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Question ID VK-103793