Let `f'(x) ={(|x|) , (1):} underset(x=0)(0le|x|le2).` Examine the behaviour of f(x) at x=0.

Explanation

To examine the behavior of the function \( f(x) \) at \( x = 0 \), we start with the given derivative:

\[
f'(x) =
\begin{cases}
|x| & \text{for } 0 \leq |x| \leq 2 \\
1 & \text{for } x = 0
\end{cases}
...