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When a graph of a function is concave up?
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In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain elements. Equivalently, a concave function is any function for which the hypograph is convex.
Nov 14, 2023 · A concave function is a function for which any secant line (a line connecting two points on the function) lies below the function. The shape of a concave...
- To discern from a graph whether a function is concave, draw secant lines (lines connecting two points on the function). If they lie below the funct...
- A concave function's secant lines lie below the function, while a convex function's secant lines lie above the function. A concave function's secon...
- A concave function is a function whose secant lines lie below the function. Additionally, a concave function is a function whose second derivative...
Dec 21, 2020 · The graph of a function \(f\) is concave up when \(f'\) is increasing. That means as one looks at a concave up graph from left to right, the slopes of the tangent lines will be increasing. Consider Figure \(\PageIndex{1}\), where a concave up graph is shown along with some tangent lines.
If the line is below the curve, the graph is concave. A Level AQA Edexcel OCR. Points of Inflexion. A point of inflexion occurs when the curve transitions from convex to concave or vice versa. We’re looking for sections of the graph where f'' (x) = 0.
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.
Graphically, a function is concave up if its graph is curved with the opening upward (Figure \(\PageIndex{1a}\)). Similarly, a function is concave down if its graph opens downward (Figure \(\PageIndex{1b}\)).
Apr 18, 2023 · In this mathematics article, we will study what is concave functions, their graphs, methods for determining convexity or concavity, techniques for identifying concavity, and properties of concave functions through worked-out examples.
