Locate the turning points of the curve y=x(x^2 - 12) and determine their nature.
$\displaystyle y = x^3 - 12x$.
Solve $\displaystyle \frac{dy}{dx} = 0$ to get x-coordinates of stationary points.
Use the sign test to test the nature of each stationary point.
Substitute each solution for x back into $\displaystyle y = x^3 - 12x$ to get the corresponding y-coordinate.