By using Equation $(3\mathrm{.}21)-$ Show, with all steps clearly documented, that the Laplace transform of the second derivative of $f(t)$ is given by $s^{2}F(s)-sf(0)-f^{\text{'}}(0)$ where $F(s)$ is the Laplace $t{r}_i$

The following theorem is the basis of using Laplace transform to solve LTI ODEs.

$L(\frac{df(t)}{dt})=F^{\text{'}}(s)=sF(s)-f(0)$