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

The correct option is B $R-\left\{1\right\}$

From the graph we can see that the function is continuous everywhere in $R$ but have a sharp corner at $x=1$.

So, it is not differentiable at $x=1$

So, the function is differentiable in $R-\left\{1\right\}$