| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Find stationary points coordinates |
| Difficulty | Moderate -0.3 This is a straightforward application of chain rule (part i) and quotient rule (part ii) followed by solving dy/dx = 0. Both are standard textbook exercises with routine algebraic manipulation, making it slightly easier than average, though the quotient rule with ln x requires some care. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
4 For each of the following curves, find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ and determine the exact $x$-coordinate of the stationary point:\\
(i) $y = \left( 4 x ^ { 2 } + 1 \right) ^ { 5 }$,\\
(ii) $y = \frac { x ^ { 2 } } { \ln x }$.
\hfill \mbox{\textit{OCR C3 2009 Q4 [7]}}