+图钭学技术大荸数学系 University of Science and Technology of china DEPARTMENT OF MATHEMATICS 例:给定点列{x,f(x)2且x2一x=x-=h,求 f(x2),f"(x),f(x0) 解: X-X(x-x X-XoX-x. L2(x) f(x1) x-x0)(x-x1) x 2h h 2h2 +x-x2) L2(x) x-xx-x. x f(x)+ 0 x-x+x-x 2f(x1)+ f(x2 2h h 2h2数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 给定点列   2 0 ( , ( )) i i i= x f x 且 x2 − x1 = x1 − x0 = h ，求 '( ), '( ), '( ) 2 1 0 f x f x f x 解： ( ) 2 ( )( ) ( ) ( )( ) ( ) 2 ( )( ) ( ) 2 2 0 1 2 1 0 2 2 0 1 2 2 f x h x x x x f x h x x x x f x h x x x x L x − − + − − − + − − = ( ) 2 ( ) ( ) ( ) ( ) 2 ( ) ' ( ) 2 2 0 1 2 1 0 2 2 0 1 2 2 f x h x x x x f x h x x x x f x h x x x x L x − + − + − − + − + − + − = 例：