A polynomial that agrees with f and all its derivatives at one point

This instrument shows how Pₙ(x) = Σ f⁽ᵏ⁾(a)/k! · (x−a)ᵏ builds a local polynomial approximation of f(x) around an expansion point a. Pick a function, drag the center a or the order n, and watch the copper curve fold itself onto the teal one — and watch it fall apart again outside the radius of convergence.