Which of the following functions differentiable at x = 0 ? - Vidyadip

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 $f(x)=\sin (|x|)-|x|$

$\Rightarrow \quad f(x)=\left\{\begin{array}{ll}{\sin x-x:} & {x \geq 0} \\ {-\sin x+x ;} & {x<0}\end{array}\right.$

$\therefore \quad {f^\prime }\left( {{0^ + }} \right) = 0 = {f^\prime }\left( {{0^ - }} \right)$

$\Rightarrow \quad f(x)$ is differentiable at $x=0$

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