Answer
When we zoom in toward the point $(0,1)$, we can see that the graph makes a smooth line through the point. This shows us that $g$ is differentiable at the point $(0,1)$
When we zoom in toward the point $(-1,0)$ and the point $(1,0)$, we can see that the graph comes to a sharp point. This shows us that $g$ is not differentiable at the point $(-1,0)$ or $(1,0)$
Work Step by Step
$g(x) = (x^2-1)^{2/3}$
When we zoom in toward the point $(0,1)$, we can see that the graph makes a smooth line through the point. This shows us that $g$ is differentiable at the point $(0,1)$
When we zoom in toward the point $(-1,0)$ and the point $(1,0)$, we can see that the graph comes to a sharp point. This shows us that $g$ is not differentiable at the point $(-1,0)$ or $(1,0)$
