I am getting stuck with the following problem :

Let f be a real-valued function continuous

**on the closed interval**[0,1] and differentiable on

**(0,1)**with f(0)=1 and f(1)=0. which of the following must be true :

I . There exists x in

**(0,1)**st. f(x)=x

II.There exists x in

**(0,1)**st. f'(x)=-1

III. f(x)>0 for all x in

**[0,1)**

(A) I only

(B) II only

(C) I and II only

(D) II and III only

(E) I, II, III

Whey said "on the closed interval [0,1]" does it mean that : f :[0,1] -->[0,1] ?

thanks so much