Mathslive.ie

DIFFERENTIATION

Exam Cog
SLOPE

m = (y₂-y₁)/(x₂-x₁)

y=mx+c → m · ax+by+c=0 → -a/b

y = xⁿ → dy/dx = n xⁿ⁻¹

SLOPE AT A POINT

Differentiate, then sub the x in

Tangent: y - y₁ = m(x - x₁)

TURNING POINTS

dy/dx = 0 → turning point

d²y/dx² > 0 min · < 0 max

Increasing dy/dx>0 · Decreasing <0

SKETCHING

Roots: y = 0 (formula)

Mark roots + turning point, draw

MOTION

v = ds/dt [m/s]

a = d²s/dt² [m/s²]

initial = t=0 · at rest = ds/dt=0