Monotonicity_JEE-MAIN_08-01-2020_S1 - Competishun – Live JEE & NEET Courses and Exam Prep

JEE MAIN 2020

08-01-20 S1

Question

Let $f(x)=x \cos ^{-1}(-\sin |x|), x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, then which of the following is true?

Select the correct option:

$f^{\prime}(0)=-\frac{\pi}{2}$

$f^{\prime}$ is decreasing in $\left(-\frac{\pi}{2}, 0\right)$ and increasing in $\left(0, \frac{\pi}{2}\right)$

f is not differentiable at $\mathrm{x}=0$

$f^{\prime}$ is increasing in $\left(-\frac{\pi}{2}, 0\right)$ and decreasing in $\left(0, \frac{\pi}{2}\right)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Medium

Start Preparing for JEE with Competishun