An inflection point of a smooth plane curve is a point where its signed curvature changes sign. At a regular inflection point the curvature vanishes.
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An inflection point is a point on a curve where the curvature changes sign. In other words, it is a point at which the curve transitions from being concave (curved upwards) to convex (curved downwards), or vice versa. This concept is crucial in calculus and helps in understanding the behavior of functions. In mathematical terms, for a function \( f(x) \): 1. The second derivative \( f''(x) \) exists at the point of interest.