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?
real-analysis continuity
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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?
real-analysis continuity
Take any continuous function not derivable and take then the integral of it.
â Piquito
Aug 20 at 12:20
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up vote
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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?
real-analysis continuity
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?
real-analysis continuity
asked Aug 20 at 12:07
Tensor_Product
779415
779415
Take any continuous function not derivable and take then the integral of it.
â Piquito
Aug 20 at 12:20
add a comment |Â
Take any continuous function not derivable and take then the integral of it.
â Piquito
Aug 20 at 12:20
Take any continuous function not derivable and take then the integral of it.
â Piquito
Aug 20 at 12:20
Take any continuous function not derivable and take then the integral of it.
â Piquito
Aug 20 at 12:20
add a comment |Â
1 Answer
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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
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
add a comment |Â
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.
add a comment |Â
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.
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.
answered Aug 20 at 12:12
nicomezi
3,6721819
3,6721819
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Take any continuous function not derivable and take then the integral of it.
â Piquito
Aug 20 at 12:20