| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | February |
| Marks | 4 |
| Topic | Differentiation from First Principles |
| Type | First principles: polynomial with multiple terms |
| Difficulty | Moderate -0.5 This is a straightforward application of the first principles definition to a simple polynomial. While it requires careful algebraic manipulation and understanding of limits, it's a standard textbook exercise with no conceptual surprises—slightly easier than average because the polynomial is simple (only two terms, low degree) and the technique is routine for students who have practiced it. |
| Spec | 1.07g Differentiation from first principles: for small positive integer powers of x |
2.\\
$f ( x ) = 3 x ^ { 2 } + 2 x . \quad$ Find $f ^ { \prime } ( x )$ from first principles.\\
(4)\\
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q2 [4]}}