# Characteristics of Lagrange remainder in Taylor formula

Taylor formula (assuming $$x_0 = 0$$) for function $$f$$ with Lagrange remainder is $$f(x) = f(0) + \frac{f'(0)}{1!}x + \frac{f”(0)}{2!}x^2 + … + \frac{f^{(n)}(0)}{n!}x^n + \frac{f^{(n+1)}(c)}{(n+1)!}x^{n+1}$$, where $$c \in (0, x)$$ if $$x > 0$$ and $$c \in (x, 0)$$ if $$x < 0$$.

Is there any characterization of $$c$$? Can we tell anything about what $$c$$ might be or might not be, except that it’s in this interval? Sometimes when solving problems I feel like I could simplify my solutions if I’d known something more about this $$c$$.