Question

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

• A. continuous and differentiable at x = 0
• B. $\underset{x\to -\infty }{Lim}$ f (x) = 0
• C. one local maxima and one local minima
• D. Decreasing function in (0,1)

Answer 1

The correct option is A continuous and differentiable at x = 0

Let $f\left(x\right)=\{\begin{array}{cc}{e}^x,& x\le 0\\ |1-x|& x>0\end{array}$

${lim}_{x\to -\infty }{e}^x=0$

${lim}_{x\to -\infty }|1-x|=\infty$

At $x=0,e^x=e^0=1,|1-x|=|1-0|=1$