2019 TMJC P1 Q5

It is given that \(\mathrm{f}(x)=4x-{{x}^{3}}\).

1. On separate diagrams, sketch the graphs of \(y=\left| \mathrm{f}(x) \right|\) and \(y-\left( \left| x \right| \right)\), showing clearly the coordinates of any axial intercept(s) and turning point(s).[4]
2. Find the exact value of the constant \(k\) for which \(\displaystyle\displaystyle \displaystyle\int_{0}^{k}{\left| \mathrm{f}(x) \right|}\mathrm{ d}x=\displaystyle\displaystyle \displaystyle\int_{-2}^{2}{\mathrm{f}\left( \left| x \right| \right)\mathrm{d}x}\).[4]