| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Topic | Tangents, normals and gradients |
| Type | Determine nature of stationary points |
| Difficulty | Moderate -0.8 This is a straightforward differentiation and stationary point question using basic power rule and standard techniques. Part (a) requires simple differentiation of polynomial and fractional power terms. Part (b) involves setting the derivative to zero (solving a simple equation), finding coordinates, and using second derivative test or gradient analysis. All steps are routine A-level procedures with no problem-solving insight required, making it easier than average but not trivial due to the fractional power. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives |
A curve is defined for $x \geq 0$ by the equation
$$y = 6x - 2x^{\frac{1}{2}}$$
\begin{enumerate}[label=(\alph*)]
\item Find $\frac{dy}{dx}$. [2 marks]
\item The curve has one stationary point. Find the coordinates of the stationary point and determine whether it is a maximum or minimum point. Fully justify your answer. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2022 Q12 [5]}}