| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2024 |
| Session | October |
| Marks | 5 |
| Topic | Differentiation from First Principles |
| Type | First principles: polynomial (find gradient) |
| Difficulty | Moderate -0.5 This is a straightforward application of the first principles formula to a simple polynomial (2x² - 3) at a specific point. While it requires careful algebraic manipulation, it's a standard textbook exercise with no conceptual difficulty beyond applying the definition of the derivative. The simplicity of the polynomial and evaluating at a single point makes it easier than average. |
| Spec | 1.07g Differentiation from first principles: for small positive integer powers of x |
\begin{enumerate}
\item The quadratic polynomial $2 x ^ { 2 } - 3$ is denoted by $f ( x )$.
\end{enumerate}
Use differentiation from first principles to determine the value of $f ^ { \prime } ( 2 )$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2024 Q1 [5]}}