AQA Paper 3 2021 June — Question 9

Exam BoardAQA
ModulePaper 3 (Paper 3)
Year2021
SessionJune
TopicDifferentiation Applications
TypeFind second derivative

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