Find the turning points on the curve with the equation y=x^4-12x^2
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)
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