Further Applications of Differentiation (AQA A-Level Mathematics): Flashcards

Function is concave up, graph bends upwards like U

Function is concave down, graph bends downwards like upside-down U

Point where concavity changes from up to down or vice versa

Solve $f''(x) = 0$ or where $f''(x)$ is undefined, then verify sign change

$f'(c) = 0$ and $f''(c) > 0$

$f'(c) = 0$ and $f''(c) < 0$

When $f'(x) = 0$ and $f''(x) = 0$

Acceleration: a(t) = rac{d^2s(t)}{dt^2}

At critical point where $P''(x) < 0$ (concave down)

At critical point where $C''(x) > 0$ (concave up)