$$\begin{aligned} &f^{\prime}(x) \geq 0, f^{\prime \prime}(x)=f(x)\\ &\text { Second order differential equation } \end{aligned}$$

$$\begin{aligned} & f(x)=A e^x+B e^{-x} \\ & f(0)=0 \Rightarrow A=-B \\ & \Rightarrow f(x)=A\left(e^x-e^{-x}\right) \\ & f^{\prime}(x)=A e^x+A e^{-x}=A\left(e^x+e^{-x}\right) \\ & f^{\prime}(0)=3=A\left(e^0+e^{-0}\right)=2 A \Rightarrow A=\frac{3}{2} \\ & f(x)=\frac{3}{2}\left(e^x-e^{-x}\right) \\ & \text { If }(\ln 3)=\frac{27}{2}\left(e^{\ln 3}-e^{-\ln 3}\right)=\frac{27}{2}\left(3-\frac{1}{3}\right)=\frac{27}{2} \cdot \frac{8}{3} \\ & =36 \end{aligned}$$