Differentiation

m = (y₂-y₁)/(x₂-x₁). y=mx+c → slope m. ax+by+c=0 → m = -a/b.

y = xⁿ → dy/dx = n xⁿ⁻¹. Multiply by the power, reduce by 1. Constant → 0. dy/dx = slope.

Differentiate, then substitute the x-value.

Need a point and a slope. Slope from dy/dx; equation y - y₁ = m(x - x₁).

Set dy/dx equal to what you're told and solve. For an unknown letter, sub the known x and slope in.

dy/dx = 0 for the turning point. d²y/dx² > 0 → min; < 0 → max.

Increasing where dy/dx > 0; decreasing where dy/dx < 0.

Find the roots (y = 0) and the turning point (dy/dx = 0). Mark them and draw the curve.

v = ds/dt [m/s]; a = d²s/dt² [m/s²]. Initial = t=0; at rest = ds/dt = 0.