Tough derivative definition

1. Jun 2, 2014

joshmccraney

hey pf!

can you help me with this $$\lim_{h \to 0} \frac{f(x+3h^2) - f(x-h^2)}{2h^2}$$

i know the definition and have tried several substitutions, but no help. anyone have any ideas?

2. Jun 2, 2014

joshmccraney

nevermind, lopitals rule did the trick

3. Jun 2, 2014

lurflurf

hint 1
$$0=\mathrm{f}(x)-\mathrm{f}(x)$$
hint 2
$$\lim_{h \to 0} \frac{f(x+3h^2) - f(x-h^2)}{2h^2}=\lim_{h \to 0}\left[\frac{3}{2}\frac{\mathrm{f}(x+3h^2)-\mathrm{f}(x)}{3h^2}+\frac{1}{2}\frac{\mathrm{f}(x-h^2)-\mathrm{f}(x)}{-h^2}\right]$$