| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Find stationary points coordinates |
| Difficulty | Moderate -0.3 This is a straightforward stationary points question requiring basic differentiation of power functions and solving simple equations. Finding point A involves solving a factorized equation, and finding B requires standard differentiation and solving dy/dx = 0. Slightly easier than average due to the simple algebraic manipulation involved. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives |
6.
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The diagram shows the curve with equation $y = 3 x - x ^ { \frac { 3 } { 2 } } , x \geq 0$.
The curve meets the $x$-axis at the origin and at the point $A$ and has a maximum at the point $B$.\\
(i) Find the $x$-coordinate of $A$.\\
(ii) Find the coordinates of $B$.\\
\hfill \mbox{\textit{OCR C1 Q6 [8]}}