Let f(x), f″(x), f″(x) denote a function of x, its first and second derivatives respectively. If f(x), f″(x) are one-valued, finite and continuous, and f″(x) exists in the neighbourhood of the value a of x, then

where o < θ < I. Suppose the value a is an approximation to a root of the equation f(x) = o, the true value of which is a + h. Equation (I) becomes

and supposing that f″(a) ≠ o

that is, a + h differs from .