How To Determine Maximum And Minimum Points From A Changing Second Derivative

inflection point

switch from concave up to concave down or vice versa

An inflection point on a curve is a point where the curvature changes sign. In other words, the curve changes from being convex to concave, or vice versa. Mathematically, an inflection point is a point where the second derivative of a function changes sign.

Graphically, an inflection point is indicated by a change in the curvature of the curve. When a curve is concave upwards (the curvature is positive), the inflection point is the point at which the curve changes to concave downwards (the curvature is negative). Conversely, when a curve is concave downwards (the curvature is negative), the inflection point is the point at which the curve changes to concave upwards (the curvature is positive).

Inflection points can be useful in analyzing functions, as they occur at points where the behavior or direction of the curve changes. For example, an inflection point can indicate a change in the rate of growth or a transition from increasing to decreasing.

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