| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Find curve equation from derivative |
| Difficulty | Moderate -0.3 This is a straightforward integration and differentiation question requiring standard techniques: differentiating a sum of powers (including negative powers), integrating to find f(x) using the constant of integration, and proving monotonicity by showing f'(x) > 0. All parts are routine C3 calculus with no problem-solving insight needed, making it slightly easier than average. |
| 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 Q1 [10]}}