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Math Help - maximum value problem

  1. #1
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    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.
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  2. #2
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    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.
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  3. #3
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    Re: maximum value problem

    Quote Originally Posted by piscoau View Post
    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
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  4. #4
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    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}
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  5. #5
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    Re: maximum value problem

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