For an infinitely differentiable function $f$ and $h>0$, if the approximated derivative $$D_hf(x)=\frac{\alpha f(x)+\beta(f(x+h)-f(x-h))+\gamma(f(x+2h)-f(x-2h))}{h}$$
yields error $f'(x)-D_hf(x)=Ch^4$, where $C$ is a constant, then the value of $\alpha , \beta , \gamma$
I find the value of $\alpha=0 , \beta=2/3 , \gamma=\frac{-1}{12}$, Can someone please check that my answer is correct or not. Thanks.