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How to calculate the slope in the curve
Slope in the curve? A little lax.

The radius of curvature of a curve at a certain point?

The slope of the tangent of the curve at a certain point?

For the slope of the tangent, find the derivative function (that is, the tangent of the inclination angle of the tangent), and then substitute the data of this point.

Radius of curvature, see attached figure.