| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2021 |
| Session | November |
| Marks | 5 |
| Topic | Stationary points and optimisation |
| Type | Find stationary points coordinates |
| Difficulty | Standard +0.3 This is a straightforward stationary points question requiring product rule differentiation and solving a factored cubic equation. While it involves multiple steps (product rule with a chain rule component, setting dy/dx = 0, and factoring), these are standard A-level techniques with no conceptual difficulty beyond routine calculus. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07q Product and quotient rules: differentiation |
In this question you must show detailed algebraic reasoning.
Find the coordinates of any stationary points on the curve below.
$$y = (1 - 3x)(3 - x)^3$$
[5]
\hfill \mbox{\textit{SPS SPS SM 2021 Q3 [5]}}