If $f$ is differentiable at $k$, find: $\lim_{h \to 0} \frac{f(k + ph) - f(k - ph)}{h}$
I realize that since the limit exists at k, then:
$\lim_{h \to 0} \frac{f(k + h) - f(k)}{h} = f'(k)$
and I can visualize what might be happening on the coordinate axis: the two point on each axis are getting further apart it seems?
But I'm not sure how this has all affected the limit in the question.