For the function f(x)=e^(sin |x|)-|x|, x, consider the following statements: Statement I: f is differentiable for all x. Statement II: f is increasing in (-π,-(π)/2). In the light of the above statements, choose the correct answer from the options given below:

(A) Both Statement I and Statement II are true

(B) Both Statement I and Statement II are false

(C) Statement I is true but Statement II is false

(D) Statement I is false but Statement II is true

Limit, Continuity and Differentiability: JEE Main 2026 Mathematics question

JEE Main 2026 · 8 Apr, Evening shift · Q13

JEE Main 20268 Apr, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

For the function

f(x)=e^{\sin|x|}-|x|

x\in\mathbb{R}

, consider the following statements : Statement I:

f

is differentiable for all

x\in\mathbb{R}

. Statement II:

f

is increasing in

\left(-\pi,-\frac{\pi}{2}\right)

. In the light of the above statements, choose the correct answer from the options given below :

JEE Main 2026 Limit, Continuity and Differentiability Question with Solution (8 Apr Evening shift, Q13) | JEE Arc