The derivative may be viewed as a transformation. In this animation, the function $f(x)$ is shown in a traditional graph along with its tangent line at $x=c$. In addition, it is shown as a transformation of the number line into the number line in the bottom two graphs. In the bottom graph, when the derivative is largest the area around $c$ expands the most and when small (near $0$) the expansion is smaller. This visualization approach from a 3brown1blue video.
$c =$