(f(x0+h)-f(x0-h))/2h=(f(x0+h)-f(x0)+f(x0)-f(x0-h))/2h=1/2 * ( ((fx0+h)-f(x0))/h + ((fx0-h)-f(x0))/(-h) )=1/2 ( f'(x0) + f'(x0) )= f'(x0)