Confusion in understanding Taylors theorem.

[AAQIB IQBAL]

I know that Taylors theorem is used to expand f(a+h) in terms of f(a) and its derivatives in the interval (a,a+h), but my question is that can we use it to expand f(a-h) in terms of f(a) and its derivatives over the interval (a-h,a).
If yes please give reason.

 

[tiny-tim]

Hi AAQIB IQBAL!

Define g(x) = f(2a - x), so g(a + h) = f(a - h),

and then apply Taylor's theorem to g ​

 

[HallsofIvy]

Or- replace the coefficients of odd powers of h, in the expansion of x+h with their negatives.