Let f be continuous on the closed and bounded interval [a,b] and let x1, x2, .... , xn be in [a,b]. Show that there must exist a c in [a,b] such that f(c) =

f(x1) + f(x2) + .... + f(xn)

----------------------------------------.

n

I think all I have to show is that:

minimum value of f(x) in [a,b] is less than or equal to the expression above which is less than or equal to the maximum value of f(x) in [a,b]. But how do I show that this is true? Then, I can just use the Intermediate Value Theorem to prove that a f(c) exists.

Thank you for any help (the ------------ is obviously a division sign).