1. ## maximum value problem

Find an example of a continuous function $f:[a,b] \in R$, where $a,b \in Q$, such that: 1) $f(q)\in Q$for every rational $q\in [a,b]$; 2) the restriction of f to Q $\cap [a,b]$ does not attain a maximum value.

2. ## Re: maximum value problem

1) Any polynomials equation with rational coefficient , such as x^5+x^3+x^2-10=y
2) I don't understand what are you talking about.

3. ## Re: maximum value problem

Originally Posted by piscoau
1) Any polynomials equation with rational coefficient , such as x^5+x^3+x^2-10=y
2) I don't understand what are you talking about.
part b states the rational points in [a,b] which does not attain a maximum value, such as the maximum value is irrational, the example needs to satisfied both of the conditions.
So, a general polynomials equation will not work

4. ## Re: maximum value problem

what i have in mind is a function with sub interval such as f={ x when x not = 0} = {0 when x=0}

5. ## Re: maximum value problem

i think the function $f(x)= x^3 - 5$ will work for $x \in[-7/5, 7/5]$