Hello,(adsbygoogle = window.adsbygoogle || []).push({});

according to my textbook, the Taylor expansion offirst orderof a scalar functionf(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question on Taylor expansion of first order

**Physics Forums | Science Articles, Homework Help, Discussion**