Homework:

Find a formula for $C[f^{\text{'}\text{'}}(t)]$ in terms of $C[f(t)]$ and the constants $f(0)$ and $f^{\text{'}}(0).$

Instructions:

Write on paper the calculations needed to find the formula for $L[f^{\text{'}\text{'}}(t)].$

Once you have the whole calculation on paper, then use it to complete the following problem.

Select only $4$ of the following options in the correct order.

Choose from these options.

$=(sL[f]+f(0))+f^{\text{'}}(0)$

$=sL[f^{\text{'}}]$

$=s^{2}L[f]+s{f}^{\text{'}}(0)+f(0)$

$=sL[f^{\text{'}}]+f^{\text{'}}(0)$

$=s^{2}L[f]+sf(0)+f^{\text{'}}(0)$

$=sL[f]+f^{\text{'}}(0)$

$=s(sL[f]-f^{\text{'}}(0))-f(0)$

$$

$=s(sL[f]-f(0))-f^{\text{'}}(0)$

Drag and drop the correct options in the right order.

$L[f^{\text{'}\text{'}}]=$

$=L[(f^{\text{'}}{)}^{\text{'}}]$

$=sL[f^{\text{'}}]-f(0)$

$=sL[f^{\text{'}}]-f^{\text{'}}(0)$

$=s^{2}L[f]-sf(0)-f^{\text{'}}(0)$