Thread: maximum value problem

Find an example of a continuous function , where , such that: 1) for every rational ; 2) the restriction of f to Q does not attain a maximum value.

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.

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

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

i think the function will work for