question_answer

Let \[f(x)=\left\{ \begin{matrix}    {{e}^{x}}, & x\le 0  \\    \left| 1-x \right|, & x>0  \\ \end{matrix} \right.\], then which of the following statement is INCORRECT?

A)  \[f\] is continuous and differentiable at \[x=0\].

B) \[\underset{x\to -\infty }{\mathop{\lim }}\,f(x)=0\]

C)  \[f\] has one local maxima and one local minima

D)  \[f\] is decreasing function in (0, 1).

Correct Answer: A

Solution :

From graph