Question

Suppose that f is continuous on [0,1] and that f(0) = f(1). Show that there is a point \[c \in [0, 1/2]\]such that\[f(c) = f(c+1/2)\]#If I draw this as a symmetric graph, I can see how this works, but what if it is not symmetric?

Answer 1

is this Supposed to be right for all functions?

Answer 2

because it doesn't work for \(f(x)=x\) for example