3.
$$f ( x ) = a x ^ { 3 } - x ^ { 2 } + b x + 4$$
where \(a\) and \(b\) are constants.
When \(\mathrm { f } ( x )\) is divided by ( \(x + 4\) ), the remainder is - 108
- Use the remainder theorem to show that
$$16 a + b = 24$$
Given also that ( \(2 x - 1\) ) is a factor of \(\mathrm { f } ( x )\),
- find the value of \(a\) and the value of \(b\).
- Find \(\mathrm { f } ^ { \prime } ( x )\).
- Hence find the exact coordinates of the stationary points of the curve with equation \(y = \mathrm { f } ( x )\).
| VIXV SIHIANI III IM IONOO | VIAV SIHI NI JYHAM ION OO | VI4V SIHI NI JLIYM ION OO |