- #1

- 713

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according to my textbook, the Taylor expansion of

*first order*of a scalar function

*f(t)*having continuous 2nd order derivative is supposed be: [tex]f(t) = f(0) + f'(0)t + \frac{1}{2}f''(t^*)t^2[/tex] for some [itex]t^*[/itex] such that [itex]0\leq t^* \leq 1[/itex]

Quite frankly, I have never seen such a formulation and I don't understand how one could derive the identity [tex]\frac{1}{2}f''(t^*)t^2 = \frac{1}{2}f''(0)t^2 + \frac{1}{3!}f'''(0)t^3 + \frac{1}{4!}f''''(0)t^4 + \ldots [/tex]

Can anyone help me with this?