Let f:[0,1]→[0,1]f: [0, 1] \to [0, 1]f:[0,1]→[0,1] be continuous. Which of the following is true?
There exists c∈[0,1]c \in [0, 1]c∈[0,1] such that f(c)=0f(c) = 0f(c)=0.
There exists c∈[0,1]c \in [0, 1]c∈[0,1] such that f(c)=cf(c) = cf(c)=c.
There exists c∈[0,1]c \in [0, 1]c∈[0,1] such that f(c)=1f(c) = 1f(c)=1.
All of the above are true.