As you might think, maximum curvature does occur at the stationary points, but it does not. You can find the exact values of x which are quite surprising and give you an insight as to how the curve behaves.

Bang on! It's so weird. The curve actually flattens out "slightly" between 1.0091 and 1. If asked this question I would have thought, off the top of my head, for sure the stationary point.

Bang on! It's so weird. The curve actually flattens out "slightly" between 1.0091 and 1. If asked this question I would have thought, off the top of my head, for sure the stationary point.

Or -1.00908