小雯 asked in 科學數學 · 9 years ago

有人會中間值定理的証明嗎?

let f : [a,b]對應到[a,b] be continuous on the whole interval [a,b]

show by 中間值定理 there exists a point c屬於[a,b] such that f(c)=c

1 Answer

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  • Sam
    Lv 6
    9 years ago
    Favorite Answer

    Consider F(x) = f(x)-x.We know thatF(a)=f(a)-a >=0 and F(b)=f(b)-b<=0.So 0 is in F(b)and F(a).By Intermediate value theorem,

    there is c in a and b such that F(c ) = 0, i.e. f(c)-c=0, or f(c) =c.[[Done]]

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