On the value regions of systems $\{f(z_1),f'(z_1)\}$ and $\{f(z_1),f(z_2)\}$ in the class of typically real functions

In the class $T$ consisting of regular and typically real functions in the disk $|x|<1$, the value regions of the system $\{f(z_1),f'(z_1)\}$ and $\{f(z_1),f(z_2)\}$ are found for fixed $z_1$ and $z_2$. As an application, the value regions of $f'(z_1)$ and $f(z_2)$ are found for $f\in T$ with fixed value $f(z_1)$.