Show that the function `f(x)=2x-|x|` is continuous but not differentiable at `x=0`

Explanation

To show that the function \( f(x) = 2x - |x| \) is continuous but not differentiable at \( x = 0 \), we will follow these steps:

### Step 1: Define the function for different intervals
The function \( f(x) = 2x - |x| \) can be expressed differently depending on the value of \( x \):
- For \( x < 0 \):
\[ |x| = -x \quad \Rightarrow \quad f(x) = 2x - (-x) = 2x + x = 3x \]
...