If f ′ (x0) = - 2, then Lim [f (x0 + H) - f (x0-h)] / h=

If f ′ (x0) = - 2, then Lim [f (x0 + H) - f (x0-h)] / h=

lim(h->0){[f(x0+h)-f(x0-h)]/h}
=lim(h->0){[f(x0+h)-f(x0)+f(x0)-f(x0-h)]/h}
=lim(h->0){[f(x0+h)-f(x0)]/h}+lim(h->0){[f(x0-h)-f(x0)]/(-h)}
=F '(x0) + F' (x0) (defined by derivative)
=2f'(x0)
=2*(-2) (∵f′(x0)=-2)
=-4.