Find the Maclaurin series for fx using the definition of a M

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. (assume that f has a power series expansion)

F(x)=4e^(3x)

Find the associated radius of convergence, R

R=?

f (x) = 4e^(3x) f (0) = 4 f \' = 12e^(3x) f \'(0) = 12 f \'\' = 36e^(3x) f \'\'(0) = 36 f \'\'\' = 108e^(3x) f \'\'\'(0) = 108 f \'\'\'\' = 324e^(3x) f \'\'\'\'(0) = 324 f(x) = 4 + 12x/2! + 36x^2/3! + 108x^3/4! + 324x^4/5! + .......