Calc Review for Mini-Flashcard 8: Concavity and Points of Inflection

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What is a point of inflection?

Back

A point of inflection is a point on the graph of a function where the concavity changes, meaning the function changes from concave up to concave down or vice versa.

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How do you determine concavity of a function?

Back

To determine concavity, find the second derivative of the function. If the second derivative is positive on an interval, the function is concave up; if negative, it is concave down.

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What is the second derivative test for concavity?

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How do you find points of inflection?

Back

To find points of inflection, set the second derivative equal to zero and solve for x. Check the sign of the second derivative around these points to confirm a change in concavity.

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What is the significance of a point of inflection in a graph?

Back

A point of inflection indicates a change in the direction of curvature of the graph, which can signify a change in the behavior of the function.

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There are no points of inflection for this function.

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What does it mean if a function is concave up?

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If a function is concave up, it means that the graph of the function is curving upwards, and the slope of the tangent line is increasing.

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What does it mean if a function is concave down?

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If a function is concave down, it means that the graph of the function is curving downwards, and the slope of the tangent line is decreasing.