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Question:

Consider the functions, 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).

Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1

Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

Statement 1 is true, Statement 2 is false.

Statement 1 is false, Statement 2 is true

Solution:

f(x) = |x - 2| + |x - 5|
f(x) is a constant function in [2, 5], f is continuous in [2, 5] and differentiable in (2, 5) and f(2) = f(5).
f'(4) = 0 by Rolle's theorem.
Hence, option 'B' is correct.