$(30$ points$)$ Analytically derive the order of accuracy for the following finite$-$difference formulas. Assume uniform distribution of points with a step size $h.$

$($a$)$

$f^{\text{'}}(x_i)=\frac{3f(x_i)-4f(x_{i-1})+f(x_{i-2})}{2h}$

$($b$)$

$f^{\text{'}\text{'}}(x_i)=\frac{-f(x_{i+3})+4f(x_{i+2})-5f(x_{i+1})+2f(x_i)}{h^2}$