7.
$$f ( x ) = x ^ { 4 } - 4 x - 8$$
- Show that there is a root of \(\mathrm { f } ( x ) = 0\) in the interval \([ - 2 , - 1 ]\).
- Find the coordinates of the turning point on the graph of \(y = \mathrm { f } ( x )\).
- Given that \(\mathrm { f } ( x ) = ( x - 2 ) \left( x ^ { 3 } + a x ^ { 2 } + b x + c \right)\), find the values of the constants, \(a , b\) and \(c\).
- In the space provided on page 21, sketch the graph of \(y = \mathrm { f } ( x )\).
- Hence sketch the graph of \(y = | \mathrm { f } ( x ) |\).