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- Mathematically, a curve is concave up if its second derivative is positive, and concave down if its second derivative is negative. Essentially, concavity describes the shape of a curve at a specific point, indicating whether it's curving upward or downward.
www.geeksforgeeks.org/concavity-and-points-of-inflection/
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Nov 16, 2022 · The second derivative will allow us to determine where the graph of a function is concave up and concave down. The second derivative will also allow us to identify any inflection points (i.e. where concavity changes) that a function may have.
Dec 21, 2020 · If we are trying to understand the shape of the graph of a function, knowing where it is concave up and concave down helps us to get a more accurate picture. Of particular interest are points at which the concavity changes from up to down or down to up; such points are called inflection points.
The concavity of the graph of a function refers to the curvature of the graph over an interval; this curvature is described as being concave up or concave down. Generally, a concave up curve has a shape resembling "∪" and a concave down curve has a shape resembling "∩" as shown in the figure below. Concave up.
If we are trying to understand the shape of the graph of a function, knowing where it is concave up and concave down helps us to get a more accurate picture. Of particular interest are points at which the concavity changes from up to down or down to up; such points are called inflection points .
Concavity and convexity. It is said that a function f (x) is convex if, once having joined any two points of the graph, the segment stays over the graph: In this graph we can observe different segments (with different colors) that join two points of the graph and stay over it.
Inflection points, concavity upward and downward. A point of inflection of the graph of a function f f is a point where the second derivative f′′ f ″ is 0 0. We have to wait a minute to clarify the geometric meaning of this. A piece of the graph of f f is concave upward if the curve ‘bends’ upward.
If a function changes from concave upward to concave downward or vice versa around a point, it is called a point of inflection of the function. In determining intervals where a function is concave upward or concave downward, you first find domain values where f″ (x) = 0 or f″ (x) does not exist.
