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

$f(x)$ is increasing if $f(x_1) \leq f(x_2)$ for $x_1 < x_2$.

$f(x)$ is decreasing if $f(x_1) > f(x_2)$ for $x_1 < x_2$.

$f(x)$ is strictly increasing if $f(x_1) < f(x_2)$ for $x_1 < x_2$.

$f(x)$ is strictly decreasing if $f(x_1) > f(x_2)$ for $x_1 < x_2$.

$f'(x) > 0$ means $f(x)$ is increasing; $f'(x) < 0$ means decreasing.

Critical points occur where $f'(x) = 0$ or is undefined.

Use test points in intervals defined by critical points.

$f(x)$ is constant on intervals where $f'(x) = 0$.

Calculate the first derivative $f'(x)$ of the function.

Finding local maxima or minima using increasing/decreasing info.