Consider the function $f(x) = {-x}^{3} - 3x^{2} + 5x + 7$ and its graph $F$.

\begin{enumerate}
\item
  \nbPointsEnumi{6}Draw a table of signs showing the variations of function $f$.
\item
  \nbPointsEnumi{2}Find the coordinates of the turning points of $F$ and state their
  nature. Give answers correct to 1 d.p.
\item
  \nbPointsEnumi{2}Find the equation of the tangent to the graph at \(x = -1\).
\item
  \nbPointsEnumi{2}Find the coordinates of the points on $F$ where the tangent has
  slope 5.
\item
  \nbPointsEnumi{2}Find the equation of the tangents to $F$ with slope 5.
\end{enumerate}
