Let `f'(x) ={[|x| , 0lt|x|le2],[1, x=0]} .` Examine the behaviour of f(x) at x=0.

Explanation

To examine the behavior of the function \( f(x) \) at \( x = 0 \) given the derivative \( f'(x) \), we will follow these steps:

### Step 1: Define the derivative \( f'(x) \)

The derivative is given as:
\[
f'(x) =
\begin{cases}
...