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.

## math for fun

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Edited: Sep 20, 2020

# Find the values of x where the curve f(x) = x^3 - 3x achieves maximum curvature.

Find the values of x where the curve f(x) = x^3 - 3x achieves maximum curvature.

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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