Thread: Proof of a maximum and minimum

A function f is said to be increasing on a set S if the inequality f(t) is less than or equal to f(x) holds whenever t and x belong to S and t is less than or equal to x. Prove that every increasing function on the interval [0,1] must have both a max and a min.

What can you say about f(1)? And what can you say about f(0)?

Originally Posted by Slazenger3

A function f is said to be increasing on a set S if the inequality f(t) is less than or equal to f(x) holds whenever t and x belong to S and t is less than or equal to x. Prove that every increasing function on the interval [0,1] must have both a max and a min.

Do you want to say that the max/min occurs on the interval?

I believe so...

Then look again at JoachimAgrell's response!

Originally Posted by Slazenger3

I believe so...

To give a further hint:

Take any number in , say . Now compare to and .