Let f be a real-valued, sufficiently differentiable function on the interval I ⊂ R , c ∈ I {\displaystyle I\subset \mathbb {R} ,\;c\in I} and n ≥ 1 {\displaystyle n\geq 1} an integer. Also let all the derivatives of f at c be zero up to and including the nth derivative, but with the (n+1)th derivative being non-zero: