y = x^4 - 12x^2

dy/dx = 4x^3 - 24x

The turning points are where dy/dx = 0

4x^3 - 24x =0

x(4x^2 - 24) = 0 Therefore one of the turning points is at x = 0

4x^2 - 24 = 0

4x^2 = 24

x^2 = 6

x = +/- √6

Substitute the x coordinates back into the original equation to find y

The final coordinates are (0,0), (√6,-36) and (-√6,-36)