MCQ
Which of the following functions differentiable at $x = 0$ ?
- A$cos (|x|)+|x|$
- B$cos (|x|)-|x|$
- C$sin (|x|)+|x|$
- ✓$sin (|x|)-|x|$
✓
Answer
Correct option: D.
$sin (|x|)-|x|$
d
Let $f(x)=\sin (|x|)-|x|$
Let $f(x)=\sin (|x|)-|x|$
$\Rightarrow \quad f(x)=\left\{\begin{array}{ll}{\sin x-x:} & {x \geq 0} \\ {-\sin x+x ;} & {x<0}\end{array}\right.$
$\therefore \quad {f^\prime }\left( {{0^ + }} \right) = 0 = {f^\prime }\left( {{0^ - }} \right)$
$\Rightarrow \quad f(x)$ is differentiable at $x=0$
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