Exercise 2
\[f^{\prime}(t) = 4t^3+9t^2-24t+1\] \[f^{\prime \prime}(t) = 12t^2+18t-24\]
\[g^\prime(x) = \cos x + \sin x\] \[g^{\prime \prime}(x) = -\sin x + \cos x\]
\[\Theta^\prime(\alpha) = \mathrm{e}^\alpha + \ln \alpha\ + 1\] \[\Theta^{\prime \prime}(\alpha)=\mathrm{e}^\alpha + \frac{1}{\alpha}\]
\[x^\prime(t) = 2 \sin t \cos t + \sin t\] \[x^{\prime \prime}(t) = 2(\cos^2(t)-\sin^2(t)) + \sin t\]