Find the coordinates of the minimum point of the curve $y = x^3 - 6x^2 + 9x$.

$\dfrac{dy}{dx} = 3x^2 - 12x + 9 = 3(x - 1)(x - 3)$, which is zero at $x = 1$ and $x = 3$. The second derivative is $6x - 12$: negative at $x = 1$ (a maximum, where $y = 4$) and positive at $x = 3$ (a minimum, where $y = 27 - 54 + 27 = 0$). The point $(1, 4)$ is the maximum, not the minimum, and $(2, 2)$ is the point of inflexion.