Local linearity

Local linearity is a trait in most differentiable graphs. The property means that the graph will seem more and more like a straight line (equal to the derivative at that point) the more and more you zoom in. You can use local linearity to approximate slopes.

If $x \approx a$,then:

$f'(a) \approx \frac {f(x)-f(a)}{x-a}$

We assume that $f^{(2)}(x) = f^{(2)}(a) = 0$