Determine whether the given statement is true or false.
If a function $k$ is continuous at $d$, then $k$ must be differentiable at $d$?

• A. True, since continuity ensures a smooth curve
• B. False, since a function can be continuous but have a sharp corner at $d$
• C. True, because differentiability is a consequence of continuity
• D. False, because continuity only means the function has no breaks at $d$

Answer: (B)