Question

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

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

Answer 1

Answer: (C)

$a+b=0$

Given, $f\left(x\right)=a\sin \left|x\right|+b{e}^{\left|x\right|}$

We know that $\sin \left|x\right|$ and $e^{\left|x\right|}$ is not differentiable at $x=0$

Therefore, for $f\left(x\right)$ to differentiable at $x=0$, we must have $a=b=0$.

$\therefore a+b=0$