Let $f$ be continuously differentiable on $\mathbb { R }$. Let $f _ { n } ( x ) = n \left( f \left( x + \frac { 1 } { n } \right) - f ( x ) \right)$. Then,\\
(a) $f _ { n }$ converges uniformly on $\mathbb { R }$;\\
(b) $f _ { n }$ converges on $\mathbb { R }$, but not necessarily uniformly;\\
(c) $f _ { n }$ converges to the derivative of $f$ uniformly on $[ 0,1 ]$;\\
(d) there is no guarantee that $f _ { n }$ converges on any open interval.