# Find the supremum, infinum, maximum and minimum

## Homework Statement

find the supremum, infinum, maximum and minimum

## Homework Equations

(n-2sqrt(n)) n is element of natural numbers

## The Attempt at a Solution

no idea on how to do this help please

Drawing the graph is always a good idea. You know the graph of y=x and i assume also the graph of 2*x^1/2. After that you can easily sketch x-2*x^2 and then you'll probably have a better idea were to look

Disconnected
Gold Member

Do you know the definition of sup, inf, max and min, or is it just this question in particular that is causing problems?

its this question in particular that's giving me the headache

Disconnected
Gold Member

Well, what is the smallest natural number? What is the value of the function at that point? Does the function increase or decrease from that point? Does it converse or diverge?

## Homework Equations

(n-2sqrt(n)) n is element of natural numbers

Why don't you try finding the critical points for the related function $f(x) = x - 2 \sqrt{x}$ for real numbers and then restricting your answer to the naturals? This would also provide you with an easy way to use Disconnected's idea of examining when the function is increasing and decreasing.