Answer
When we zoom in toward the point $(-1,0)$, we can see that the graph makes a smooth line through the point. This shows us that $f$ is differentiable at the point $(-1,0)$
When we zoom in toward the origin at $(0,0)$, we can see that the graph comes to a sharp point. This shows us that $f$ is not differentiable at the point $(0,0)$
Work Step by Step
$f(x) = x+\sqrt{\vert x \vert}$
When we zoom in toward the point $(-1,0)$, we can see that the graph makes a smooth line through the point. This shows us that $f$ is differentiable at the point $(-1,0)$
When we zoom in toward the origin at $(0,0)$, we can see that the graph comes to a sharp point. This shows us that $f$ is not differentiable at the point $(0,0)$
