Consider the following three statements for the function f:(0,∞) defined by f(x)=| log e x|-|x-1|: (I) f is differentiable at all x>0. (II) f is increasing in (0,1). (III) f is decreasing in (1,∞). Then.

(A) Only (I) and (III) are TRUE.

(B) Only (II) and (III) are TRUE.

(C) All (I), (II) and (III) are TRUE.

Limit, Continuity and Differentiability: JEE Main 2026 Mathematics question

JEE Main 2026 · 24 Jan, Evening shift · Q6

JEE Main 202624 Jan, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Consider the following three statements for the function

f:(0,\infty)\to\mathbb{R}

defined by

f(x)=|\log_e x|-|x-1|

: (I)

f

is differentiable at all

x>0

. (II)

f

is increasing in

(0,1)

. (III)

f

is decreasing in

(1,\infty)

. Then.