Thread: Continuous function

f: [0,2]--->R be a continuous function on [0,2]. And f(0)=f(2).
Show that there is a c in (0,1) such that f(c)=f(c+1).

(hint: g(x)=f(x)-f(x+1))

Originally Posted by alper82

f: [0,2]--->R be a continuous function on [0,2]. And f(0)=f(2).
Show that there is a c in (0,1) such that f(c)=f(c+1).

(hint: g(x)=f(x)-f(x+1))

Note that:

1. g(0) = f(0) - f(1) and g(1) = f(1) - f(2) = f(1) - f(0) = - g(0).

2. g(x) is continuous.

Apply the Intermediate Value Theorem.