The derivative peak slides toward 0 without ever getting shorter

1. A.$(f_n{)}_n{\ge }_1$ converges uniformly to 0 on $\mathbb{R}$, and $(f_n^{\prime }{)}_n{\ge }_1$ converges uniformly to 0 on the interval (−M, M) for some positive real number M.
2. B.$(f_n{)}_n{\ge }_1$ converges uniformly to 0 on $\mathbb{R}$, and $(f_n^{\prime }{)}_n{\ge }_1$ converges pointwise to 0 on $\mathbb{R}$.✓
3. C.$(f_n{)}_n{\ge }_1$ converges uniformly to 0 on $\mathbb{R}$ and $(f_n^{\prime }{)}_n{\ge }_1$ does not converge pointwise to 0 on $\mathbb{R}$.
4. D.$(f_n{)}_n{\ge }_1$ converges pointwise to 0 on $\mathbb{R}$ but not uniformly on $\mathbb{R}$.

The trap it tests

Pointwise vs uniform

The mode of convergence — or of continuity — was the wrong one.