Sketching Gradient Functions (AQA A-Level Mathematics): Flashcards

Slope of original function at each point

$f'(x) > 0$, above $x$-axis

$f'(x) < 0$, below $x$-axis

$f'(x) = 0$, crosses $x$-axis

From positive to negative

From negative to positive

$f'(x)$ is increasing

$f'(x)$ is decreasing

Reaches min/max, doesn't cross $x$-axis

Smooth curve without sharp corners