Taylor expansion based problem [closed]
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If $f(0)=0$ and $f''(x)$ exists in $[0,infty)$, show that
$$
f'(x)-frac{f(x)}{x}=frac{1}{2}xf''(xi),
qquad
0<xi<x,
$$
and deduce that if $f'(x)>0$ for $x>0$, $f(x)/x$ is strictly increasing.
taylor-expansion
edited Nov 14 at 13:15
egreg
173k1383198
asked Nov 14 at 13:04
Shashank
2
closed as off-topic by Gibbs, José Carlos Santos, Jam, ancientmathematician, amWhy Nov 14 at 17:03
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Gibbs, José Carlos Santos, ancientmathematician, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
-2
down vote
favorite
If $f(0)=0$ and $f''(x)$ exists in $[0,infty)$, show that
$$
f'(x)-frac{f(x)}{x}=frac{1}{2}xf''(xi),
qquad
0<xi<x,
$$
and deduce that if $f'(x)>0$ for $x>0$, $f(x)/x$ is strictly increasing.
taylor-expansion
edited Nov 14 at 13:15
egreg
173k1383198
asked Nov 14 at 13:04
Shashank
2
closed as off-topic by Gibbs, José Carlos Santos, Jam, ancientmathematician, amWhy Nov 14 at 17:03
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Gibbs, José Carlos Santos, ancientmathematician, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
Hello, welcome to math.SE. Please use Mathjax to format your equations and Show what you've tried so far. I'm voting to close this question as off-topic because you haven't shown what you've tried.
– Jam
Nov 14 at 13:28
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
If $f(0)=0$ and $f''(x)$ exists in $[0,infty)$, show that
$$
f'(x)-frac{f(x)}{x}=frac{1}{2}xf''(xi),
qquad
0<xi<x,
$$
and deduce that if $f'(x)>0$ for $x>0$, $f(x)/x$ is strictly increasing.
taylor-expansion
edited Nov 14 at 13:15
egreg
173k1383198
asked Nov 14 at 13:04
Shashank
2
If $f(0)=0$ and $f''(x)$ exists in $[0,infty)$, show that
$$
f'(x)-frac{f(x)}{x}=frac{1}{2}xf''(xi),
qquad
0<xi<x,
$$
and deduce that if $f'(x)>0$ for $x>0$, $f(x)/x$ is strictly increasing.
taylor-expansion
taylor-expansion
edited Nov 14 at 13:15
egreg
173k1383198
asked Nov 14 at 13:04
Shashank
2
edited Nov 14 at 13:15
egreg
173k1383198
asked Nov 14 at 13:04
Shashank
2
edited Nov 14 at 13:15
egreg
173k1383198
edited Nov 14 at 13:15
egreg
173k1383198
edited Nov 14 at 13:15
egreg
173k1383198
173k1383198
asked Nov 14 at 13:04
Shashank
2
asked Nov 14 at 13:04
Shashank
2
asked Nov 14 at 13:04
Shashank
2
2
closed as off-topic by Gibbs, José Carlos Santos, Jam, ancientmathematician, amWhy Nov 14 at 17:03
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Gibbs, José Carlos Santos, ancientmathematician, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Gibbs, José Carlos Santos, Jam, ancientmathematician, amWhy Nov 14 at 17:03
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Gibbs, José Carlos Santos, ancientmathematician, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
Hello, welcome to math.SE. Please use Mathjax to format your equations and Show what you've tried so far. I'm voting to close this question as off-topic because you haven't shown what you've tried.
– Jam
Nov 14 at 13:28
add a comment |
Hello, welcome to math.SE. Please use Mathjax to format your equations and Show what you've tried so far. I'm voting to close this question as off-topic because you haven't shown what you've tried.
– Jam
Nov 14 at 13:28
Hello, welcome to math.SE. Please use Mathjax to format your equations and Show what you've tried so far. I'm voting to close this question as off-topic because you haven't shown what you've tried.
– Jam
Nov 14 at 13:28
Hello, welcome to math.SE. Please use Mathjax to format your equations and Show what you've tried so far. I'm voting to close this question as off-topic because you haven't shown what you've tried.
– Jam
Nov 14 at 13:28
add a comment |
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Hello, welcome to math.SE. Please use Mathjax to format your equations and Show what you've tried so far. I'm voting to close this question as off-topic because you haven't shown what you've tried.
– Jam
Nov 14 at 13:28