- #1
FsLiu
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- 0
Homework Statement
Find f'(0) given a piecewise function defined as
f(x) =
{g(x)/x2, x≠0
{0, x=0
where g(x) is a function satisfying g(0)=g'(0)=g''(0) and g'''(0)=14
Homework Equations
none.
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