| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Increasing/decreasing intervals |
| Difficulty | Standard +0.3 This is a straightforward integration and differentiation question testing standard C3 techniques. Part (a) requires one differentiation, part (b) is routine integration with a constant to find, and part (c) requires showing f'(x) > 0 using AM-GM inequality or completing the square—slightly above average due to the proof element but still a standard exercise. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07o Increasing/decreasing: functions using sign of dy/dx1.08b Integrate x^n: where n != -1 and sums |
The function f, defined for $x \in \mathbb{R}, x > 0$, is such that
$$f'(x) = x^2 - 2 + \frac{1}{x^2}$$
\begin{enumerate}[label=(\alph*)]
\item Find the value of f''(x) at $x = 4$. [3]
\item Given that f(3) = 0, find f(x). [4]
\item Prove that f is an increasing function. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q6 [10]}}