inflection point
switch from concave up to concave down or vice versa
In calculus, an inflection point is a point on a curve where the rate of change switches from increasing to decreasing, or vice versa. In other words, it’s a point where the concavity of a curve changes. Mathematically speaking, an inflection point is a point where the second derivative of the function changes sign.
For example, if we have a curve that is concave up (meaning its second derivative is positive) to the left of a certain point and concave down (meaning its second derivative is negative) to the right of that point, then that point is an inflection point.
Inflection points are important in calculus because they can be used to analyze the behavior of functions and find important features such as maximum and minimum values, points of inflection, and the shape of the curve. They are also important in applications such as economics, physics, and engineering where they can be used to find the optimal values of certain variables.
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