Methods2024 NHT Exam 2 Section A · Q19CAS active1 mark

Sign of a product involving a derivative

Graph of y = f(x), a continuous curve decreasing steeply from the top left, crossing the x-axis at (−2, 0), reaching a local minimum at (−1, f(−1)) below the axis, passing through the origin (0, 0), rising to a local maximum at (3, f(3)), then falling to cross the x-axis at (4, 0) and continuing downward.

Let $f: R \to R$ be a continuous and differentiable function. Part of the graph of $f$ is shown below.

The stationary points of $f$ are at $\left(-1, f(-1)\right)$ and $\left(3, f(3)\right)$ .

The solution to the inequality $(x^2 - x - 2)f'(x) > 0$ is

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