Let $f$ be a real differenciable function such that $|f(x+h)-f(x)|leq |h|g(h)$ with $h,xinmathbb{R}$ and...
Show that $f$ is a constant function in $mathbb{R}$.
How I did:
$frac{f(x+h)-f(x)}{|h|}leq g(h)Rightarrow lim_{hrightarrow0} frac{f(x+h)-f(x)}{|h|}leqlim_{hrightarrow0} g(h)Rightarrow f'(x)leq 0$.
Question: What should I do to have $ f '(x) = 0 $?
calculus functions
asked Nov 27 '18 at 16:33
Juliana de Souza
656
add a comment |
Show that $f$ is a constant function in $mathbb{R}$.
How I did:
$frac{f(x+h)-f(x)}{|h|}leq g(h)Rightarrow lim_{hrightarrow0} frac{f(x+h)-f(x)}{|h|}leqlim_{hrightarrow0} g(h)Rightarrow f'(x)leq 0$.
Question: What should I do to have $ f '(x) = 0 $?
calculus functions
asked Nov 27 '18 at 16:33
Juliana de Souza
656
2
You have forgotten a pair of |.
– xbh
Nov 27 '18 at 16:34
1
You should remember the absolute value sign in the question that you forgot.
– user3482749
Nov 27 '18 at 16:35
I knew it was something obvious that was missing! Thanks a lot!
– Juliana de Souza
Nov 27 '18 at 16:42
add a comment |
Show that $f$ is a constant function in $mathbb{R}$.
How I did:
$frac{f(x+h)-f(x)}{|h|}leq g(h)Rightarrow lim_{hrightarrow0} frac{f(x+h)-f(x)}{|h|}leqlim_{hrightarrow0} g(h)Rightarrow f'(x)leq 0$.
Question: What should I do to have $ f '(x) = 0 $?
calculus functions
asked Nov 27 '18 at 16:33
Juliana de Souza
656
Show that $f$ is a constant function in $mathbb{R}$.
How I did:
$frac{f(x+h)-f(x)}{|h|}leq g(h)Rightarrow lim_{hrightarrow0} frac{f(x+h)-f(x)}{|h|}leqlim_{hrightarrow0} g(h)Rightarrow f'(x)leq 0$.
Question: What should I do to have $ f '(x) = 0 $?
calculus functions
calculus functions
asked Nov 27 '18 at 16:33
Juliana de Souza
656
asked Nov 27 '18 at 16:33
Juliana de Souza
656
asked Nov 27 '18 at 16:33
Juliana de Souza
656
asked Nov 27 '18 at 16:33
Juliana de Souza
656
asked Nov 27 '18 at 16:33
Juliana de Souza
656
656
2
You have forgotten a pair of |.
– xbh
Nov 27 '18 at 16:34
1
You should remember the absolute value sign in the question that you forgot.
– user3482749
Nov 27 '18 at 16:35
I knew it was something obvious that was missing! Thanks a lot!
– Juliana de Souza
Nov 27 '18 at 16:42
add a comment |
2
You have forgotten a pair of |.
– xbh
Nov 27 '18 at 16:34
1
You should remember the absolute value sign in the question that you forgot.
– user3482749
Nov 27 '18 at 16:35
I knew it was something obvious that was missing! Thanks a lot!
– Juliana de Souza
Nov 27 '18 at 16:42
2
2
You have forgotten a pair of |.
– xbh
Nov 27 '18 at 16:34
You have forgotten a pair of |.
– xbh
Nov 27 '18 at 16:34
1
1
You should remember the absolute value sign in the question that you forgot.
– user3482749
Nov 27 '18 at 16:35
You should remember the absolute value sign in the question that you forgot.
– user3482749
Nov 27 '18 at 16:35
I knew it was something obvious that was missing! Thanks a lot!
– Juliana de Souza
Nov 27 '18 at 16:42
I knew it was something obvious that was missing! Thanks a lot!
– Juliana de Souza
Nov 27 '18 at 16:42
add a comment |
1 Answer
1
active
oldest
votes
Fix an $x$. What can you say about
$$left|{f(x+h)-f(x)over h}right|$$
when $hto0>$?
answered Nov 27 '18 at 17:30
Christian Blatter
172k7112325
add a comment |
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1 Answer
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1 Answer
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active
oldest
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active
oldest
votes
active
oldest
votes
Fix an $x$. What can you say about
$$left|{f(x+h)-f(x)over h}right|$$
when $hto0>$?
answered Nov 27 '18 at 17:30
Christian Blatter
172k7112325
add a comment |
Fix an $x$. What can you say about
$$left|{f(x+h)-f(x)over h}right|$$
when $hto0>$?
answered Nov 27 '18 at 17:30
Christian Blatter
172k7112325
add a comment |
Fix an $x$. What can you say about
$$left|{f(x+h)-f(x)over h}right|$$
when $hto0>$?
answered Nov 27 '18 at 17:30
Christian Blatter
172k7112325
Fix an $x$. What can you say about
$$left|{f(x+h)-f(x)over h}right|$$
when $hto0>$?
answered Nov 27 '18 at 17:30
Christian Blatter
172k7112325
answered Nov 27 '18 at 17:30
Christian Blatter
172k7112325
answered Nov 27 '18 at 17:30
Christian Blatter
172k7112325
answered Nov 27 '18 at 17:30
Christian Blatter
172k7112325
172k7112325
add a comment |
add a comment |
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2
You have forgotten a pair of |.
– xbh
Nov 27 '18 at 16:34
1
You should remember the absolute value sign in the question that you forgot.
– user3482749
Nov 27 '18 at 16:35
I knew it was something obvious that was missing! Thanks a lot!
– Juliana de Souza
Nov 27 '18 at 16:42