| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Second derivative and nature determination |
| Difficulty | Moderate -0.8 This is a straightforward differentiation question requiring basic power rule application (rewriting terms as powers) and routine second derivative calculation at a specific point. It's easier than average as it involves only mechanical differentiation with no problem-solving, though the rewriting step (x^{-1} and x^{1/2}) requires minimal algebraic manipulation. |
| Spec | 1.07d Second derivatives: d^2y/dx^2 notation1.07i Differentiate x^n: for rational n and sums1.07l Derivative of ln(x): and related functions |
9 Given that $\mathrm { f } ( x ) = \frac { 1 } { x } - \sqrt { x } + 3$,\\
(i) find $\mathrm { f } ^ { \prime } ( x )$,\\
(ii) find $\mathrm { f } ^ { \prime \prime } ( 4 )$.
\hfill \mbox{\textit{OCR C1 2010 Q9 [8]}}