| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | September |
| Marks | 6 |
| Topic | Stationary points and optimisation |
| Type | Prove or show increasing/decreasing function |
| Difficulty | Standard +0.3 This is a straightforward application of differentiation to prove monotonicity. Students must find f'(x) using quotient rule or rewriting as x^(-5) - 2x^4, then show f'(x) < 0 for x > 0. The algebra is routine and the conclusion direct, making it slightly easier than average but requiring proper justification for full marks. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07o Increasing/decreasing: functions using sign of dy/dx |
2.\\
$f ( x ) = \frac { 1 - 2 x ^ { 9 } } { x ^ { 5 } } \quad$ for $x > 0$
Prove that $f ( x )$ is a decreasing function.\\[0pt]
[6 marks]\\
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q2 [6]}}