I have the function $\dfrac{dx}{dt} = f(y - x)$, where $y$ and $x$ are functions of $t$. We also have that $f(0) = 0$.
It then says,
Now, any reasonable function has a tangent line approximation, and since $f(0) = 0$, we have $f(z) \approx kz$. That is, when $|z|$ is fairly small, $f(z)$ is fairly close to $kz$. (From calculus you know that $k = f'(0)$, but we won't use that here).
I understand that we have $f(0) = 0$, but I don't understand the section
... we have $f(z) \approx kz$. That is, when $|z|$ is fairly small, $f(z)$ is fairly close to $kz$. (From calculus you know that $k = f'(0)$, but we won't use that here).
I would greatly appreciate it if people could please take the time to help me understand this.