Last updated on Oct 23, 2026

Concavity and Points of Inflection (HSC SSCE Mathematics Advanced): Flashcards

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Concavity and Points of Inflection

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Concavity determined by

Sign of second derivative $f''(x)$

$f''(a) > 0$ means curve is

Concave up

$f''(a) < 0$ means curve is

Concave down

Memory aid: concave up shape

Cup ( $\cup$ ) - can hold water

Point of inflection is where

Tangent crosses curve

Two conditions for point of inflection

$f''(x) = 0$ AND $f''(x)$ changes sign

Inflectional tangent

Tangent at point of inflection

$f'(a) = 0$ , $f''(a) > 0$ gives

Minimum turning point

$f'(a) = 0$ , $f''(a) < 0$ gives

Maximum turning point

$f'(a) = 0$ , $f''(a) = 0$ means 2nd derivative test is

Inconclusive

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Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Quizzes by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Exam Questions by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

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