Last updated on Oct 23, 2026

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

Concavity and Points of Inflection

Practise the questions

10 questions from this quiz

Cup that can hold water ( $\cup$ )

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

No, concavity must also change sign

Maximum turning point

Minimum turning point

When $f''(a) = 0$

Evaluate $f'(a)$

At zeroes or discontinuities of $f''(x)$

Crosses the curve

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

Practise the questions

If f′′(a)>0f''(a) > 0f′′(a)>0, what is the concavity of the curve at x=ax = ax=a?

Which shape best describes a curve that is concave up?

What TWO conditions are required for a point of inflection?

Is f′′(x)=0f''(x) = 0f′′(x)=0 sufficient to guarantee a point of inflection?

If f′(a)=0f'(a) = 0f′(a)=0 and f′′(a)<0f''(a) < 0f′′(a)<0, what is at x=ax = ax=a?

If f′(a)=0f'(a) = 0f′(a)=0 and f′′(a)>0f''(a) > 0f′′(a)>0, what is at x=ax = ax=a?

When is the second derivative test inconclusive for a stationary point?

How do you find the gradient of an inflectional tangent at x=ax = ax=a?

Where can f′′(x)f''(x)f′′(x) change sign?

A point of inflection is where the tangent does what to the curve?

Explore HSC SSCE Mathematics Advanced Revision Notes 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

Displaying and Interpreting Data

Continuous Probability Distributions

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

Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Flashcards 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

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

Displaying and Interpreting Data

Continuous Probability Distributions

Join 100,000+ SSCE students studying Quizzes with us.

If $f''(a) > 0$ , what is the concavity of the curve at $x = a$ ?

Is $f''(x) = 0$ sufficient to guarantee a point of inflection?

If $f'(a) = 0$ and $f''(a) < 0$ , what is at $x = a$ ?

If $f'(a) = 0$ and $f''(a) > 0$ , what is at $x = a$ ?

How do you find the gradient of an inflectional tangent at $x = a$ ?

Where can $f''(x)$ change sign?