Connecting Differentiability and Continuity Practice Test

Yes; redefining one point never affects differentiability.

Yes; $\sin x$ is differentiable, so $f'(0)$ exists.

No; $f$ is discontinuous at $0$, so $f'(0)$ does not exist.

Yes; discontinuity implies a vertical tangent, so $f'(0)$ exists.

No; there is a corner at $0$, so $f'(0)$ does not exist.