Increasing & Decreasing Functions (AQA A-Level Mathematics): Flashcards

$f(x_1) \leq f(x_2)$ when $x_1 < x_2$ in $I$

$f(x_1) \geq f(x_2)$ when $x_1 < x_2$ in $I$

Increasing

Decreasing

$f'(x)$ is zero or undefined

$f(x_1) < f(x_2)$ for all $x_1 < x_2$

Calculate first derivative $f'(x)$

Solve $f'(x) = 0$ and find where $f'(x)$ is undefined

Test points

Optimization (finding maximum or minimum values)