Consider the function f : (0, ∞) → (−∞, ∞) given by f(x) = x _e(x) - x + 1. Then which one of the following statements is TRUE ?

JEE Advanced 2026 Mathematics question

Consider the function f : (0, ∞) → (−∞, ∞) given by

f(x) = (x) - x + 1.

Then which one of the following statements is TRUE ?

(A)The derivative of the function f is decreasing in the interval (0, 1)
(B)The function f has a local maximum at some point a ∈ (0, ∞)
(C)The function f has a local minimum at some point b ∈ (0, ∞)
(D)The function f has NEITHER a point of local maximum NOR a point of local minimum in the interval (0, ∞)Correct

Answer: (D)

and . So f″ > 0 on (0, 1) (f′ increasing — (A) false) and f″ < 0 on (1, ∞). Hence f′ has its maximum at x = 1, where f′(1) = 1

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Question ID VK-104705