Derivatives as Rates of Change (HSC SSCE Mathematics Advanced): Flashcards

$f'(c)$, the derivative at that point

Gradient of tangent line at that point

$\frac{f(b) - f(a)}{b - a}$

$v(t) = \frac{dx}{dt} = x'(t) = \dot{x}$

Particle moves in positive direction

Particle is momentarily at rest

Absolute value of velocity, always non-negative

$|v(t)| = |x'(t)|$

When velocity $v(t) = 0$

Vector has magnitude & direction; scalar only magnitude