能幫我看看嗎？證明或找個反例。謝謝

f(z) is differentiable on region D. Inside D there is a line segment C with end points a and b. Proof that there is a number k, |k|<=1 and a point p on C such that f(b)-f(a)=k(b-a)f'(p), all the function and numbers are complex。

人工智能說證不了：Without additional assumptions on the function f(z), such as being entire or satisfying certain conditions, it is not possible to prove the above statement in general.

所有跟帖： 

• 看到一個可供參考的定理。 -羅擊- ♂ (81 bytes) () 03/06/2024 postreply 02:46:51

• 謝謝，我想一下。 -yma16- ♂ (0 bytes) () 03/06/2024 postreply 07:00:33

• 有一篇文章裏有 -羅擊- ♂ (81 bytes) () 03/06/2024 postreply 10:21:10

• 有定理1的證明嗎？謝謝。 -yma16- ♂ (0 bytes) () 03/06/2024 postreply 16:29:17

• 在這裏，僅供參考 -羅擊- ♂ (21 bytes) () 03/06/2024 postreply 16:55:45

• 再次感謝。 -yma16- ♂ (0 bytes) () 03/07/2024 postreply 06:54:16

• 不用客氣！ -羅擊- ♂ (0 bytes) () 03/07/2024 postreply 07:31:34