A function is given by, f(x)=e^-3x

Question

write down the third-order Taylor approximation for f(x) about x =0.
Hence, evaluate f(0.258) giving your answer to 4 decimal places.

Answer 1

f = e^-3x
f' = -3e^-3x
f'' = 9e^-3x
f''' = -27e^-3x

f(x) = 1 - 3x + 9/2 x^2 - 9/2 x^3
f(.258) = 0.4483

e^(-3*.258) = 0.4612

Answer 2

i was going around in circles and putting the wrong values.

thank you for your help. thanks.