[微分]2題mean-value

[victor7935 (victor)]

1.
 A number c is called a fixed point of f if f(c)=c.

 Prove that if f is differentiable on an interval I and f'(x)< 1

 for all x屬於I,then f has at most one fixed point in I.


2.

 Show that the equation  x^n+ax+b = 0,

 n an even positive intefer, has at most two distinct real roots.

謝謝︿︿

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 140.123.221.147
推 zptdaniel:兩題應該都可以由反證法得證