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## Homework Statement

Find f'(0) given a piecewise function defined as

f(x) =

{g(x)/x

^{2}, 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)/x

^{2}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