| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Differentiating Transcendental Functions |
| Type | Find stationary points - logarithmic functions |
| Difficulty | Challenging +1.2 This question requires logarithmic differentiation of a non-standard function (x^(x²)), which is beyond typical A-level content. However, the technique is straightforward once you take ln of both sides: ln y = x² ln x, then differentiate implicitly. The stationary point condition dy/dx = 0 leads to a simple equation. While conceptually more advanced than standard C3/C4 material, it's a direct application of a known technique with minimal algebraic complexity. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.07n Stationary points: find maxima, minima using derivatives1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
1.
$$\mathrm { f } ( x ) = x ^ { \left( x ^ { 2 } \right) } \quad x > 0$$
Use logarithms to find the $x$ coordinate of the stationary point of the curve with equation $y = \mathrm { f } ( x )$ .
\hfill \mbox{\textit{Edexcel AEA 2022 Q1 [5]}}