Question

For the function \(f(x) = \sin|x| - |x|\), \(x \in \mathbb{R}\), consider the following statements:
Statement I: \(f\) is differentiable for all \(x \in \mathbb{R}\).
Statement II: \(f\) is increasing in \((-\pi, -\pi/2)\).
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

Answer 1

The Correct Option is C