How to show the following for infinitely differentiable function. [closed]
$begingroup$
Let $f$ be a real valued infinitely differentiable function with domain $mathbb{R}$. Assume $f(0) = 0$ and $f(1) = 1$. Also $f(x)geq 0$ for all $x$. Show that there exists a positive integer $n$ and a real number $x$ such that $$f^{(n)}(x) < 0$$
real-analysis functions derivatives
asked Dec 1 '18 at 16:32
Mittal GMittal G
1,193515
$endgroup$
closed as off-topic by caverac, Davide Giraudo, José Carlos Santos, KReiser, RRL Dec 9 '18 at 3:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Davide Giraudo, José Carlos Santos, KReiser, RRL
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Let $f$ be a real valued infinitely differentiable function with domain $mathbb{R}$. Assume $f(0) = 0$ and $f(1) = 1$. Also $f(x)geq 0$ for all $x$. Show that there exists a positive integer $n$ and a real number $x$ such that $$f^{(n)}(x) < 0$$
real-analysis functions derivatives
asked Dec 1 '18 at 16:32
Mittal GMittal G
1,193515
$endgroup$
closed as off-topic by caverac, Davide Giraudo, José Carlos Santos, KReiser, RRL Dec 9 '18 at 3:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Davide Giraudo, José Carlos Santos, KReiser, RRL
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
This is Problem A5 of this year's (2018) Putnam competition. No discussions are supposed to be made public until the exam has ended!
$endgroup$
– mlerma54
Dec 1 '18 at 18:43
add a comment |
$begingroup$
Let $f$ be a real valued infinitely differentiable function with domain $mathbb{R}$. Assume $f(0) = 0$ and $f(1) = 1$. Also $f(x)geq 0$ for all $x$. Show that there exists a positive integer $n$ and a real number $x$ such that $$f^{(n)}(x) < 0$$
real-analysis functions derivatives
asked Dec 1 '18 at 16:32
Mittal GMittal G
1,193515
$endgroup$
Let $f$ be a real valued infinitely differentiable function with domain $mathbb{R}$. Assume $f(0) = 0$ and $f(1) = 1$. Also $f(x)geq 0$ for all $x$. Show that there exists a positive integer $n$ and a real number $x$ such that $$f^{(n)}(x) < 0$$
real-analysis functions derivatives
real-analysis functions derivatives
asked Dec 1 '18 at 16:32
Mittal GMittal G
1,193515
asked Dec 1 '18 at 16:32
Mittal GMittal G
1,193515
asked Dec 1 '18 at 16:32
Mittal GMittal G
1,193515
asked Dec 1 '18 at 16:32
Mittal GMittal G
1,193515
asked Dec 1 '18 at 16:32
Mittal GMittal G
1,193515
1,193515
closed as off-topic by caverac, Davide Giraudo, José Carlos Santos, KReiser, RRL Dec 9 '18 at 3:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Davide Giraudo, José Carlos Santos, KReiser, RRL
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by caverac, Davide Giraudo, José Carlos Santos, KReiser, RRL Dec 9 '18 at 3:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Davide Giraudo, José Carlos Santos, KReiser, RRL
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
This is Problem A5 of this year's (2018) Putnam competition. No discussions are supposed to be made public until the exam has ended!
$endgroup$
– mlerma54
Dec 1 '18 at 18:43
add a comment |
$begingroup$
This is Problem A5 of this year's (2018) Putnam competition. No discussions are supposed to be made public until the exam has ended!
$endgroup$
– mlerma54
Dec 1 '18 at 18:43
$begingroup$
This is Problem A5 of this year's (2018) Putnam competition. No discussions are supposed to be made public until the exam has ended!
$endgroup$
– mlerma54
Dec 1 '18 at 18:43
$begingroup$
This is Problem A5 of this year's (2018) Putnam competition. No discussions are supposed to be made public until the exam has ended!
$endgroup$
– mlerma54
Dec 1 '18 at 18:43
add a comment |
0
active
oldest
votes
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
This is Problem A5 of this year's (2018) Putnam competition. No discussions are supposed to be made public until the exam has ended!
$endgroup$
– mlerma54
Dec 1 '18 at 18:43