9 A function f is defined for all real values of \(x\) as
$$f ( x ) = x ^ { 4 } + 5 x ^ { 3 }$$
The function has exactly two stationary points when \(x = 0\) and \(x = - \frac { 15 } { 4 }\)
9
- Find \(\mathrm { f } ^ { \prime \prime } ( x )\)
9
- (ii) Determine the nature of the stationary points.
Fully justify your answer.
9 - State the range of values of \(x\) for which
$$f ( x ) = x ^ { 4 } + 5 x ^ { 3 }$$
is an increasing function.
9 - A second function g is defined for all real values of \(x\) as
$$\mathrm { g } ( x ) = x ^ { 4 } - 5 x ^ { 3 }$$
9
- State the single transformation which maps f onto g .
9
- (ii) State the range of values of \(x\) for which g is an increasing function.