F(x) = f(0) + f(0)' * x / 1! +f(0)'' * x^2 / 2! + f(0)''' * x^3 /3! + .... (1)

now

f(0) = 3

f(x)' = -1/3 *( 27 - x ) ^ ( -2/3) ,,, --> f(0)' = - 1 / 27

f(x)'' = 2/9 *( 27 - x ) ^ ( -5 /3) ,,, --> f(0)'' = 2 / 2187

f(x)''' = -10/27 *( 27 - x ) ^ ( -8/3) ,,, --> f(0)''' = 10 / 177147

.....................

now by (1) we get

f(x)= 3 - (1/27) x + 2/2187 x^2 / 2! - 10/ 177147 x^3 / 3! + ....

f(x)= 3 - (1/27) x + 1/2187 x^2 - 5 / 531441 x^3 + ....

rem:- at, when x centered at 0 , it`s becam`staylor seriesMaclaurin series