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

Gradient of tangent at that point

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

Vector (has magnitude and direction)

$v(t) = \frac{dx}{dt}$

Particle moves in negative direction

Speed = $|v(t)|$

When $v(t) = 0$

Displacement and velocity

When graph crosses the $t$-axis

When graph moves toward the $t$-axis