Cubic and rational function analysis – derivatives, extrema, asymptotes

MathematicsFunctions & GraphsAges 17–18

Plots y = ax³ + bx² + cx + d or y = (ax + b)/(cx + d) alongside a variation table built live from the sign of y'. Drag point M along the curve to see the tangent line, the derivative's sign, and the interval of monotonicity being examined; change the coefficients to make extrema appear or vanish, or to shift the vertical and horizontal asymptotes.