# Proof of a maximum and minimum

• January 28th 2010, 04:50 PM
Slazenger3
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.
• January 28th 2010, 04:59 PM
JoachimAgrell
What can you say about f(1)? And what can you say about f(0)?
• January 28th 2010, 05:02 PM
Drexel28
Quote:

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?
• January 28th 2010, 05:14 PM
Slazenger3
I believe so...
• January 29th 2010, 02:39 AM
HallsofIvy
Then look again at JoachimAgrell's response!
• January 30th 2010, 12:52 AM
h2osprey
Quote:

Originally Posted by Slazenger3
I believe so...

To give a further hint:

Take any number in $[0,1]$, say $c$. Now compare $f(c)$ to $f(0)$ and $f(1)$.