| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiating Transcendental Functions |
| Type | Find tangent line equation |
| Difficulty | Standard +0.3 This is a straightforward application of the product rule to differentiate x²ln(x), followed by substituting x=e to find the gradient and using point-slope form. It's slightly above average difficulty due to requiring the product rule with a logarithm, but it's a standard C3 exercise with no conceptual challenges beyond routine differentiation and substitution. |
| Spec | 1.07l Derivative of ln(x): and related functions1.07m Tangents and normals: gradient and equations1.07q Product and quotient rules: differentiation |
3 Find, in the form $y = m x + c$, the equation of the tangent to the curve
$$y = x ^ { 2 } \ln x$$
at the point with $x$-coordinate e.
\hfill \mbox{\textit{OCR C3 2008 Q3 [6]}}