Last updated on Sep 20, 2026

Applications of Differentiation (AQA A-Level Mathematics): Quizzes

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Increasing & Decreasing Functions

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For $f(x)$ to be increasing on interval $I$ with $x_1 < x_2$ , which condition must hold?

$f(x_1) \leq f(x_2)$

What condition defines a strictly decreasing function on interval $I$ with $x_1 < x_2$ ?

$f(x_1) > f(x_2)$

If $f'(x) > 0$ for all $x$ in an interval, what can we conclude about $f(x)$ ?

$f(x)$ is increasing

If $f'(x) = 0$ for all $x$ in an interval, what is the function's behavior?

The function is constant

Where do critical points occur for a function $f(x)$ ?

Where $f'(x)$ is zero or undefined

What is the first step to determine intervals of increase and decrease?

Find the first derivative $f'(x)$

If $f'(x) < 0$ in a test interval, what does this indicate?

The function is decreasing

For $f(x) = x^3 - 3x^2 + 2$ , what are the critical points?

$x = 0$ and $x = 2$

For $f(x) = x^3 - 3x^2 + 2$ , on which interval is the function decreasing?

$(0, 2)$

For $f(x) = \frac{1}{x}$ , on which intervals is the function decreasing?

$(-\infty, 0) \cup (0, \infty)$

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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

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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