\sethandouttitle{} \begin{enumerate} \item Differentiate the function. \begin{enumerate} \item $f(x) = x^3 - 4x+6$. \vfill \item $f(s) = \frac{-12}{s^5} + \sin(s)$. \vfill \item $f(x) = \frac{ x^2 + 4x + 3 }{\sqrt{x}}$. \vfill \end{enumerate} \item Find an equation for the tangent line of $y=3x^2 - x^3$ at $(1,2)$. \vfill \newpage \item Find the first and second derivatives of $f(x) = x^4 - 3x^3 + 16x$. \vfill \item The position function of a particle is given by $s = t^3 - 4.5 t^2 - 7t$, $t \geq 0$. \begin{enumerate} \item When does the particle reach a velocity of 5m/s? \vfill \item When is the acceleration 0? What is the signifigance of this value of $t$? \vfill \end{enumerate} \item A spherical balloon is being inflated. Find the rate of increase of the surface area ($S= 4 \pi r^2$) with respect to the radius when $r=1$, $r=2$ and $r=3$. What conclusion can you make? \vfill \end{enumerate} \allhandoutinfo