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1. • • A graph is concave up where its second derivative is positive and concave down where its second derivative is negative. Thus, the concavity changes where the second derivative is zero or undefined. Such a point is called a point of inflection.
     teachingcalculus.com/2012/10/24/concavity/

     Concavity - Teaching Calculus

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   Why do we need to know where a graph is concave?

   • 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.

   5.4: Concavity and Inflection Points - Mathematics LibreTexts

   math.libretexts.org/Bookshelves/Calculus/Calculus_(Guichard)/05:_Curve_Sketching/5.04:_Concavity_and_Inflection_Points

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   How do you know if a graph is convex or concave?

   • An easy way to test for both is to connect two points on the curve with a straight line. If the line is above the curve, the graph is convex. If the line is below the curve, the graph is concave. 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.

   Convex and Concave Curves | Revision | MME - MME Revise

   mmerevise.co.uk/a-level-maths-revision/convex-and-concave-curves/

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   Which graph represents a local minimum if a graph is concave?

   • Figure \ (\PageIndex {13}\): A graph of \ (f (x)\) in Example \ (\PageIndex {4}\). The second derivative is evaluated at each critical point. When the graph is concave up, the critical point represents a local minimum; when the graph is concave down, the critical point represents a local maximum.

   3.4: Concavity and the Second Derivative - Mathematics LibreTexts

   math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/03:_The_Graphical_Behavior_of_Functions/3.04:_Concavity_and_the_Second_Derivative

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   What does a concave up curve look like?

   • Generally, a concave up curve has a shape resembling "∪" and a concave down curve has a shape resembling "∩" as shown in the figure below. There are a number of ways to determine the concavity of a function. If given a graph of f (x) or f' (x), determining concavity is relatively simple.

   Concavity - Math.net

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   What does concavity mean in math?

   • The main concept that we’ll be discussing in this section is concavity. Concavity is easiest to see with a graph (we’ll give the mathematical definition in a bit). So, a function is concave up if it “opens” up and the function is concave down if it “opens” down. Notice as well that concavity has nothing to do with increasing or decreasing.

   Section 4.6 : The Shape of a Graph, Part II - Pauls Online Math Notes

   tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtII.aspx

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   How do you know if a function is concave?

   • Concavity is easiest to see with a graph (we’ll give the mathematical definition in a bit). So, a function is concave up if it “opens” up and the function is concave down if it “opens” down. Notice as well that concavity has nothing to do with increasing or decreasing. A function can be concave up and either increasing or decreasing.

   Section 4.6 : The Shape of a Graph, Part II - Pauls Online Math Notes

   tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtII.aspx

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3. math.libretexts.org › Bookshelves › Calculus3.4: Concavity and the Second Derivative - Mathematics LibreTexts

   math.libretexts.org › Bookshelves › Calculus

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   Dec 21, 2020 · When the graph is concave up, the critical point represents a local minimum; when the graph is concave down, the critical point represents a local maximum. We have been learning how the first and second derivatives of a function relate information about the graph of that function.

4. mmerevise.co.uk › convex-and-concave-curvesConvex and Concave Curves | Revision | MME - MME Revise

   mmerevise.co.uk › convex-and-concave-curves

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   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.

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5. math.libretexts.org › Bookshelves › Calculus4.3: How Derivatives Affect the Shape of a Graph

   math.libretexts.org › Bookshelves › Calculus

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   Nov 10, 2020 · Use concavity and inflection points to explain how the sign of the second derivative affects the shape of a function’s graph. Explain the concavity test for a function over an open interval. Explain the relationship between a function and its first and second derivatives.

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6. Videos

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     12:49

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     Concavity, Inflection Points, and Second Derivative

     4 Mar 2018

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     3:21

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     Ex: Concavity / Points of Inflection by Analyzing a Graph (Algebra Topic)

     15 Jun 2012

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     12:13

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     Calculus I - Concavity and Inflection Points - Example 1

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7. tutorial.math.lamar.edu › ShapeofGraphPtIICalculus I - The Shape of a Graph, Part II

   tutorial.math.lamar.edu › ShapeofGraphPtII

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   Nov 16, 2022 · A point \(x = c\) is called an inflection point if the function is continuous at the point and the concavity of the graph changes at that point.

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8. math.libretexts.org › Bookshelves › Calculus5.4: Concavity and Inflection Points - Mathematics LibreTexts

   math.libretexts.org › Bookshelves › Calculus

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   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.

9. courses.lumenlearning.com › calculus1 › chapterThe First Derivative Test and Concavity | Calculus I

   courses.lumenlearning.com › calculus1 › chapter

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   State the first derivative test for critical points. Use concavity and inflection points to explain how the sign of the second derivative affects the shape of a function’s graph. Explain the concavity test for a function over an open interval.

10. www.math.net › concavityConcavity - Math.net

    www.math.net › concavity

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    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.