Maximum and Minimum Turning Points (Leaving Cert Mathematics): Flashcards

Where function changes from increasing to decreasing or vice versa

Zero (horizontal)

$\frac{dy}{dx} = 0$

Find the first derivative $\frac{dy}{dx}$

Higher y-value is max, lower y-value is min

$\frac{d^2y}{dx^2} < 0$ (negative)

$\frac{d^2y}{dx^2} > 0$ (positive)

Frowning ∩ (negative second derivative)

Minimum

Maximum

$\frac{dy}{dx} > 0$

$\frac{dy}{dx} < 0$

Exactly one