The height of a cycle path over a low hill is modelled by h = 2x³ - 12x² + 18x + 4 metres, where x…

Step 1. The gradient. $\dfrac{dh}{dx} = 6x^2 - 24x + 18 = 6(x - 1)(x - 3)$.

Step 2. The level places. $\dfrac{dh}{dx} = 0$ at $x = 1$ and $x = 3$. In metres these are $100\ \text{m}$ and $300\ \text{m}$ from the start.

Step 3. The heights. $h(1) = 2 - 12 + 18 + 4 = 12\ \text{m}$ and $h(3) = 54 - 108 + 54 + 4 = 4\ \text{m}$.