CCD.NA.Diff. The Differential Estimate: Another early application of the first derivative, the differential or linear estimation is often visualized with graphs, but an alternative that presents a different connection to using motion to understand the derivative is visualized with mapping diagrams.

Considering the derivative focus point for $x=a$ allows one to consider the question of what value a linear function has for a change in $x$, $\Delta x = dx$.
To estimate $f(a + \Delta x)$ the value $f(a)$ is changed by $dy=f'(a) \Delta x = f'(a) dx$, so $f(a + \Delta x) \approx f(a) + dy = f(a) + f'(a) dx$.

Download GeoGebra file