| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | December |
| Marks | 9 |
| Topic | Chain Rule |
| Type | Determine if function is increasing/decreasing |
| Difficulty | Standard +0.3 This is a straightforward calculus question requiring the chain rule and quotient rule to find first and second derivatives. Part (a) involves showing f'(x) < 0 for x > 0, which is routine. Part (b) requires finding where f''(x) = 0 and verifying the inflection point, which is standard technique. The algebra is manageable and the question follows a predictable structure, making it slightly easier than average. |
| Spec | 1.07f Convexity/concavity: points of inflection1.07i Differentiate x^n: for rational n and sums |
9 A function f is defined for $x > 0$ by $\mathrm { f } ( x ) = \frac { 6 } { x ^ { 2 } + a }$, where $a$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Show that f is a decreasing function.
\item Find, in terms of $a$, the coordinates of the point of inflection on the curve $y = \mathrm { f } ( x )$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2018 Q9 [9]}}