Q88 / 200 · WBJEE 2014 · Mathematics

The function $f(x)=a \sin |x|+b e^{| x \mid} \quad$ is differentiable at $x=0$ when

  • A
    $3 a+b=0$
  • B
    $3 a-b=0$
  • Correct answer
    C
    $a+b=0$
  • D
    $a-b=0$

Solution

Given, $f(x)=a \sin |x|+b e^{|x|}$ We know that $\sin |x|$ and $e^{|x|}$ is not differentiable at $x=0$. Therefore, for $f(x)$ to differentiable at $x=0$, we must have $a=b=0$. $\therefore$ $$ a+b=0 $$

Hence, the correct answer is option: 'C'.

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