| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2013 |
| Session | November |
| Topic | Tangents, normals and gradients |
| Type | Determine nature of stationary points |
| Difficulty | Moderate -0.3 This is a straightforward differentiation question requiring the quotient rule and basic stationary point analysis. Part (i) is routine calculation with a given answer to verify. Part (ii) requires finding where dy/dx = 0 and using the second derivative test, all standard techniques with no conceptual challenges or novel insights required. |
| Spec | 1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07l Derivative of ln(x): and related functions1.07n Stationary points: find maxima, minima using derivatives1.07o Increasing/decreasing: functions using sign of dy/dx1.07q Product and quotient rules: differentiation |
10 A curve has equation $y = \frac { \mathrm { e } ^ { x } } { x ^ { 2 } }$. Show that\\
(i) the gradient of the curve at $x = 1$ is - e ,\\
(ii) there is a stationary point at $x = 2$ and determine its nature.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2013 Q10}}