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.
An inflection point of the graph of a differentiable real function at which its derivative is zero. It has a horizontal tangent and a change of concavity, but need not be a local maximum or minimum. For a three-times continuously differentiable function, and suffice: the expansion gives opposite signs on the two sides. The elementary example is at zero. The word “saddle” is sometimes used for this one-dimensional situation in elementary examination papers, but the usual saddle point of a scalar function has a multivariable meaning; do not merge the two concepts.
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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.