non-differentiable functions

If the function has any of the traits below on its graph at $x=c$, we say that $f(x)$ is not differentiable at $x=c$

• Corners / sharp turns: the one-sided derivatives are different
• Cusps in graph: the slope of the tangent line approaches $\infty$ from one side and $-\infty$ from the other (e.g. $x^{\frac{2}{3}}$)
• Vertical line: non-differentiable as the graph as a vertical tangent
• Discontinuity: function is not continuous at $x=c$