Show that the function `f(x)=|x+1|+|x-1|` for all `x in R` , is not differentiable at `x=-1` and `x=1` .

Explanation

To show that the function \( f(x) = |x + 1| + |x - 1| \) is not differentiable at \( x = -1 \) and \( x = 1 \), we will compute the left-hand derivative and right-hand derivative at these points and check if they are equal.

### Step 1: Check differentiability at \( x = -1 \)

**Left-hand derivative at \( x = -1 \)**:
\[ f'(-1) = \lim_{h \to 0^-} \frac{f(-1 + h) - f(-1)}{h} \]
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