| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 5 |
| Topic | Differentiation from First Principles |
| Type | First principles: x⁴ and higher power terms |
| Difficulty | Standard +0.8 Differentiating from first principles requires writing out the limit definition, expanding (x+h)^4 using binomial theorem, simplifying the difference quotient, and taking the limit as h→0. While the concept is standard AS material, it's more demanding than routine differentiation and requires careful algebraic manipulation across multiple steps, making it moderately harder than average. |
| Spec | 1.07g Differentiation from first principles: for small positive integer powers of x |
Differentiate $f(x) = x^4$ from first principles. [5]
\hfill \mbox{\textit{OCR AS Pure 2017 Q7 [5]}}