Question

The set of points, where the function $f\left(x\right)=|x-1|e^x$ is differentiable, is

• A. $R$
• B. $R-\left\{1\right\}$
• C. $R-\{-1\}$
• D. $R-\left\{0\right\}$

Answer 1

Answer: (B)

$R-\left\{1\right\}$

Given, $f\left(x\right)=|x-1|e^x$
Since, $|x-1|$ is not differentiable at $x=1$.
So, $f\left(x\right)=|x-1|e^x$ is not differentiable at $x=1$.

Thus, the function $f\left(x\right)$ is differentiable for every $x\in R$ except at $1$
Hence, the required set is $R-\left\{1\right\}$.