Stationary Points (VCE SSCE Mathematical Methods): Flashcards

$f'(a) = 0$ or $\frac{dy}{dx} = 0$

Horizontal (parallel to $x$-axis)

Local maximum, local minimum, stationary point of inflection

Positive → zero → negative

Negative → zero → positive

Same sign both sides (+ to 0 to + or - to 0 to -)

Local maximum and minimum points (function changes direction)

Find derivative $f'(x)$ or $\frac{dy}{dx}$

Test sign of $f'(x)$ either side using gradient table

Inflection: sign unchanged; turning: sign changes