Question

Let f be a function derivable of class 3, such that f(x) = -2 + 2x^2 -3x^3 + o(x3). Which one is true?
a) f(1)= -3
b) f(0)= -2 and f'(0)=0
c) f(0)= -2 and f''(0) = 2
d) x = 0 is a max
e) f'''(0) = -3

I know that c is the right answer, but why?

Answer 1

Sorry, B is the right answer.

Answer 2

if you have f(1) just write in places of x ; 1
if you have f(x)= f(0) replace any x's with 0 then solve

Answer 3

that's what I've done, but writing the x in places, doesn't help because in this case would be right both A B