| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiating Transcendental Functions |
| Type | Find tangent line equation |
| Difficulty | Standard +0.3 This is a straightforward two-part question requiring standard differentiation of exponential and logarithmic functions, finding a tangent line equation, then basic coordinate geometry to find intercepts and triangle area. All techniques are routine C3 material with no novel insight required, making it slightly easier than average. |
| Spec | 1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07l Derivative of ln(x): and related functions1.07m Tangents and normals: gradient and equations1.08e Area between curve and x-axis: using definite integrals |
3. The curve $C$ has the equation $y = 2 \mathrm { e } ^ { x } - 6 \ln x$ and passes through the point $P$ with $x$-coordinate 1.\\
(i) Find an equation for the tangent to $C$ at $P$.
The tangent to $C$ at $P$ meets the coordinate axes at the points $Q$ and $R$.\\
(ii) Show that the area of triangle $O Q R$, where $O$ is the origin, is $\frac { 9 } { 3 - \mathrm { e } }$.\\
\hfill \mbox{\textit{OCR C3 Q3 [8]}}