- #1
LagrangeEuler
- 717
- 20
Function ##f(x)=x^4## has minimum at ##x=0##.
## f'(x)=4x^3##
##f'(0)=0##
##f''(x)=12x^2##
##f''(0)=0##
##f^{(3)}(x)=24x##
##f^{(3)}(0)=0##
##f^{(4)}(0)>0##
So what is the rule? I must go to the higher derivatives if ##f'(0)=f''(0)=0##?
## f'(x)=4x^3##
##f'(0)=0##
##f''(x)=12x^2##
##f''(0)=0##
##f^{(3)}(x)=24x##
##f^{(3)}(0)=0##
##f^{(4)}(0)>0##
So what is the rule? I must go to the higher derivatives if ##f'(0)=f''(0)=0##?