Question: Let f : [ 0 , 1 ] R be a continuous function such that f ( 0 ) < f ( 1 ) .

Let f:[0,1]R be a continuous function such that f(0)<f(1).

i) Let S={f(x)0x1}. Show that S is an interval of the form [a,b].

ii) Show that there exists c[0,1] such that f(c)f(1)=(f(0)f(1))c.

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