Question

Which among the following function is not differentiable at $x=0$

• A. $f\left(x\right)=x^2$
• B. $f\left(x\right)=x+\left|x\right|$
• C. $f\left(x\right)=2x$
• D. $\sin x$

Answer 1

The correct option is B $f\left(x\right)=x+\left|x\right|$

We know that polynomial, trigonometric functions in their domain are differentiable functions.
So, $f\left(x\right)=x^2,2x,\sin x$ are differentiable functions.

As $|x|$ is not differentiable at $x=0,x+|x|$ will not be a differentiable function. (As addition of differntiable and non differentiable functions is always not differentiable)