Rates of Change (Leaving Cert Mathematics): Flashcards

How quickly one quantity changes compared to another

$\frac{dy}{dx}$

Constant and equals the slope

Varies at different points

Secant line between two points

$\frac{y_2 - y_1}{x_2 - x_1}$

Tangent line at a single point

Calculate $\frac{dy}{dx}$ and evaluate at that point

$\frac{ds}{dt}$

metres per second (m/s)

Particle moving away from fixed point

Particle moving towards fixed point

$\frac{dv}{dt}$ or $\frac{d^2s}{dt^2}$

metres per second per second (m/s²)

Velocity = 0, i.e. $\frac{ds}{dt} = 0$