Last updated on Sep 21, 2026

Points of Inflection (AQA A-Level Mathematics): Quizzes

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Points of Inflection

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What occurs at a point of inflection?

The concavity of the function changes

What must $f''(x)$ do at $x = c$ for it to be a point of inflection?

Change sign

What is the first step to find points of inflection?

Find the second derivative $f''(x)$

When is a curve concave up?

When $f''(x) > 0$

When is a curve concave down?

When $f''(x) < 0$

If there is a point of inflection at $x = c$ , what can we conclude?

$f''(c) = 0$

For $f(x) = x^3 - 3x^2 + 4x$ , where is the point of inflection?

$x = 1$

At the origin, which function has a point of inflection?

$y = x^3$

For $f(x) = x^3 - 3x^2 + x - 2$ with $f''(x) = 6x - 6$ , when is $f$ convex?

$x > 1$

What confirms $x = c$ is a point of inflection after finding $f''(c) = 0$ ?

$f''(x)$ changes sign at $x = c$

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

Explore AQA A-Level Mathematics Exam Questions by Topics

Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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