I want to find A real valued function having a continuous first derrivative for all points in domain, but with undefined higher order derivatives.

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A real valued function having a continuous first derrivative for all points in domain, but higher order derivatives are not even defined



Is there an example of such a function?







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  • Take any continuous function not derivable and take then the integral of it.
    – Piquito
    Aug 20 at 12:20














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down vote

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A real valued function having a continuous first derrivative for all points in domain, but higher order derivatives are not even defined



Is there an example of such a function?







share|cite|improve this question




















  • Take any continuous function not derivable and take then the integral of it.
    – Piquito
    Aug 20 at 12:20












up vote
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down vote

favorite









up vote
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down vote

favorite











A real valued function having a continuous first derrivative for all points in domain, but higher order derivatives are not even defined



Is there an example of such a function?







share|cite|improve this question












A real valued function having a continuous first derrivative for all points in domain, but higher order derivatives are not even defined



Is there an example of such a function?









share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 20 at 12:07









Tensor_Product

779415




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  • Take any continuous function not derivable and take then the integral of it.
    – Piquito
    Aug 20 at 12:20
















  • Take any continuous function not derivable and take then the integral of it.
    – Piquito
    Aug 20 at 12:20















Take any continuous function not derivable and take then the integral of it.
– Piquito
Aug 20 at 12:20




Take any continuous function not derivable and take then the integral of it.
– Piquito
Aug 20 at 12:20










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Consider $g$ a continuous function with no derivative at any point and let $f(x)= int_0^x g(t) dt$. Such function $g$ exists, the famous Weierstrass function is one of them.



Then $f'(x)=g(x)$ by the fondamental theorem of calculus but $f''(x)$ does not exist.






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    1 Answer
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    1 Answer
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    active

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    up vote
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    down vote













    Consider $g$ a continuous function with no derivative at any point and let $f(x)= int_0^x g(t) dt$. Such function $g$ exists, the famous Weierstrass function is one of them.



    Then $f'(x)=g(x)$ by the fondamental theorem of calculus but $f''(x)$ does not exist.






    share|cite|improve this answer
























      up vote
      1
      down vote













      Consider $g$ a continuous function with no derivative at any point and let $f(x)= int_0^x g(t) dt$. Such function $g$ exists, the famous Weierstrass function is one of them.



      Then $f'(x)=g(x)$ by the fondamental theorem of calculus but $f''(x)$ does not exist.






      share|cite|improve this answer






















        up vote
        1
        down vote










        up vote
        1
        down vote









        Consider $g$ a continuous function with no derivative at any point and let $f(x)= int_0^x g(t) dt$. Such function $g$ exists, the famous Weierstrass function is one of them.



        Then $f'(x)=g(x)$ by the fondamental theorem of calculus but $f''(x)$ does not exist.






        share|cite|improve this answer












        Consider $g$ a continuous function with no derivative at any point and let $f(x)= int_0^x g(t) dt$. Such function $g$ exists, the famous Weierstrass function is one of them.



        Then $f'(x)=g(x)$ by the fondamental theorem of calculus but $f''(x)$ does not exist.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 20 at 12:12









        nicomezi

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