Find f'(0) given a piecewise function defined as
where g(x) is a function satisfying g(0)=g'(0)=g''(0) and g'''(0)=14
The Attempt at a Solution
So far, I've reasoned that for f to be differentiable at 0, limit as x approaches 0 of g(x)/x2 is zero, and that leads to L'Hopital's rule (?). However, I get stuck after 2 derivations with 0/2 where the rule no longer applies, and I'm unable to use the fact that g'''(x)=14.
Any help would be much appreciated