Q54 / 90 · JEE Main 2012 (26 May Online) · Mathematics

If $f(x)=a|\sin x|+b e^{|x|}+c|x|^3$, where $a, b, c \in R$, is differentiable at $x=0$, then

  • A
    $a=0, b$ and $c$ are any real numbers
  • B
    $c=0, a=0, b$ is any real number
  • C
    $b=0, c=0, a$ is any real number
  • Correct answer
    D
    $a=0, b=0, c$ is any real number

Solution

$|\sin x|$ and $e^{|x|}$ are not differentiable at $x=0$ and $|x|^3$ is differentiable at $x=0$. $\therefore$ for $f(x)$ to be differentiable at $x=0$, we must have $a=0, b=0$ and $c$ is any real number.

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

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