2016/018) Show that function $f(x) = | x+2 |$ is continuous at $x = - 2$ but not differentiable at x = - 2.

We have $f(x) = | x+2 |$
or $f(x) = x + 2$ for $x >=-2$ and $f(x) = -x-2$ for $x < -2$
at x = -2 the right hand limit is 0 and the left hand limit is 0
so it is continuous at x = -2
differentiating from left we get $f'(x) = -1$ and differentiating from right $f'(x) = 1$
as left hand derivative and right hand derivative are not same of it is
not differenctiable