Mike D. answered • 12/15/20

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The solution suggested above isn't completely correct. If you plot the function suggested we have horizontal tangents at the turning points x = -1, x = +1

By implicit differentiation

2y dy/dx = 3x^{2} - 3

dy/dx = (3x^{2}-3) / 2y

dy/dx is slope of tangent line, so when tangent line is horizontal dy/dx = 0

So assuming y is non zero, dy/dx will be zero when 3x^{2} - 3 = 0, x^{2} = 1, x = +1 or x = -1