| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2020 |
| Session | June |
| Marks | 6 |
| Topic | Tangents, normals and gradients |
| Type | Increasing/decreasing intervals |
| Difficulty | Moderate -0.8 This is a straightforward differentiation question requiring basic power rule application and solving a quadratic inequality. Part (a) is routine calculus, and part (b) involves standard technique of finding where dy/dx > 0. The quadratic factorizes easily, making this easier than average with no conceptual challenges beyond textbook methods. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07o Increasing/decreasing: functions using sign of dy/dx |
A curve has equation
$$y = 2x^3 - 2x^2 - 2x + 8$$
\begin{enumerate}[label=(\alph*)]
\item Find $\frac{dy}{dx}$ [2]
\item Hence find the range of values of $x$ for which $y$ is increasing. Write your answer in set notation. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2020 Q1 [6]}}