Functions

Let \(f(x) = \frac{1}{3}x^3 - x^2 -3x\). Part of the graph of \(f\) is shown below.

There is a maximum point at \(\mathrm{A}\) and a minimum point at \(\mathrm{B} (3, -9)\).

1. Find the coordinates of \(\mathrm{A}\).[8]
2. Write down the coordinates of[6]
   1. the image of \(\mathrm{B}\) after reflection in the \(y\)-axis;
   2. the image of \(\mathrm{B}\) after translation by the vector \( \begin{pmatrix} -2 \\ 5 \end{pmatrix}\);
   3. the image of \(\mathrm{B}\) after reflection in the \(x\)-axis followed by a horizontal stretch with scale factor \(\frac{1}{2}\).