答案是3f'(a),详情如图所示
f'(x)的定义是lim(h→0) [f(x+h)-f(x)]/h =f'(x)因为f(x)在x=a处可导,所以lim(h→0) [f(a+h)-f(a)]/h = f'(a)所以lim (f(a+h)-f(a-2h))/h=lim [(f(a+h)-f(a))+(f(a)-f(a-2h))]/h=lim [f(a+h)-f(a)]/h + 2*[f(a)-f(x-2h)]/(2h)=f'(a)+2f'(a)=3f'(a)
如图中