Calculus of the mean value theorem [closed]

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If $|f(w)-f(x)|leq|w-x|$ for all values $w$ and $x$ and $f$ is a differentiable function, show that $-1leq f'(x)leq1$ for all $x$-values.

edited Nov 22 at 13:21

Gödel

1,393319

asked Nov 22 at 13:10

Pauline

closed as off-topic by Jack Lee, Rebellos, amWhy, Leucippus, Chinnapparaj R Nov 23 at 2:18

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." – Jack Lee, Rebellos, amWhy, Leucippus, Chinnapparaj R

If this question can be reworded to fit the rules in the help center, please edit the question.

what have you tried?
– Siong Thye Goh
Nov 22 at 13:11

Please edit the question.
– Akash Roy
Nov 22 at 13:12

@Siong I am a 12th grade student. Can you suggest me some books on advanced Mathematics? I am currently preparing for IIT-JEE and am from India. I will try to complete the books suggested by you
– Akash Roy
Nov 22 at 13:14

@AkashRoy perhaps ask the rest taking the same exam in the chat room I did not take the exam and I am not the right person to answer the question.
– Siong Thye Goh
Nov 22 at 13:22

I am not asking anything regarding the test. I am asking you in general what books did you follow for Maths @Siong. I am asking you since you are having high reputation count.
– Akash Roy
Nov 22 at 13:37

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up vote
-1
down vote

favorite

If $|f(w)-f(x)|leq|w-x|$ for all values $w$ and $x$ and $f$ is a differentiable function, show that $-1leq f'(x)leq1$ for all $x$-values.

edited Nov 22 at 13:21

Gödel

1,393319

asked Nov 22 at 13:10

Pauline

closed as off-topic by Jack Lee, Rebellos, amWhy, Leucippus, Chinnapparaj R Nov 23 at 2:18

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." – Jack Lee, Rebellos, amWhy, Leucippus, Chinnapparaj R

If this question can be reworded to fit the rules in the help center, please edit the question.

what have you tried?
– Siong Thye Goh
Nov 22 at 13:11

Please edit the question.
– Akash Roy
Nov 22 at 13:12

@Siong I am a 12th grade student. Can you suggest me some books on advanced Mathematics? I am currently preparing for IIT-JEE and am from India. I will try to complete the books suggested by you
– Akash Roy
Nov 22 at 13:14

@AkashRoy perhaps ask the rest taking the same exam in the chat room I did not take the exam and I am not the right person to answer the question.
– Siong Thye Goh
Nov 22 at 13:22

I am not asking anything regarding the test. I am asking you in general what books did you follow for Maths @Siong. I am asking you since you are having high reputation count.
– Akash Roy
Nov 22 at 13:37

|
show 2 more comments

up vote
-1
down vote

favorite

If $|f(w)-f(x)|leq|w-x|$ for all values $w$ and $x$ and $f$ is a differentiable function, show that $-1leq f'(x)leq1$ for all $x$-values.

edited Nov 22 at 13:21

Gödel

1,393319

asked Nov 22 at 13:10

Pauline

If $|f(w)-f(x)|leq|w-x|$ for all values $w$ and $x$ and $f$ is a differentiable function, show that $-1leq f'(x)leq1$ for all $x$-values.

calculus differential-geometry

edited Nov 22 at 13:21

Gödel

1,393319

asked Nov 22 at 13:10

Pauline

edited Nov 22 at 13:21

Gödel

1,393319

asked Nov 22 at 13:10

Pauline

edited Nov 22 at 13:21

Gödel

1,393319

edited Nov 22 at 13:21

Gödel

1,393319

edited Nov 22 at 13:21

Gödel

1,393319

asked Nov 22 at 13:10

Pauline

asked Nov 22 at 13:10

Pauline

asked Nov 22 at 13:10

Pauline

closed as off-topic by Jack Lee, Rebellos, amWhy, Leucippus, Chinnapparaj R Nov 23 at 2:18

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." – Jack Lee, Rebellos, amWhy, Leucippus, Chinnapparaj R

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Jack Lee, Rebellos, amWhy, Leucippus, Chinnapparaj R Nov 23 at 2:18

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." – Jack Lee, Rebellos, amWhy, Leucippus, Chinnapparaj R

If this question can be reworded to fit the rules in the help center, please edit the question.

what have you tried?
– Siong Thye Goh
Nov 22 at 13:11

Please edit the question.
– Akash Roy
Nov 22 at 13:12

@Siong I am a 12th grade student. Can you suggest me some books on advanced Mathematics? I am currently preparing for IIT-JEE and am from India. I will try to complete the books suggested by you
– Akash Roy
Nov 22 at 13:14

@AkashRoy perhaps ask the rest taking the same exam in the chat room I did not take the exam and I am not the right person to answer the question.
– Siong Thye Goh
Nov 22 at 13:22

I am not asking anything regarding the test. I am asking you in general what books did you follow for Maths @Siong. I am asking you since you are having high reputation count.
– Akash Roy
Nov 22 at 13:37

|
show 2 more comments

what have you tried?
– Siong Thye Goh
Nov 22 at 13:11

Please edit the question.
– Akash Roy
Nov 22 at 13:12

@Siong I am a 12th grade student. Can you suggest me some books on advanced Mathematics? I am currently preparing for IIT-JEE and am from India. I will try to complete the books suggested by you
– Akash Roy
Nov 22 at 13:14

@AkashRoy perhaps ask the rest taking the same exam in the chat room I did not take the exam and I am not the right person to answer the question.
– Siong Thye Goh
Nov 22 at 13:22

I am not asking anything regarding the test. I am asking you in general what books did you follow for Maths @Siong. I am asking you since you are having high reputation count.
– Akash Roy
Nov 22 at 13:37

what have you tried?
– Siong Thye Goh
Nov 22 at 13:11

Please edit the question.
– Akash Roy
Nov 22 at 13:12

@Siong I am a 12th grade student. Can you suggest me some books on advanced Mathematics? I am currently preparing for IIT-JEE and am from India. I will try to complete the books suggested by you
– Akash Roy
Nov 22 at 13:14

@AkashRoy perhaps ask the rest taking the same exam in the chat room I did not take the exam and I am not the right person to answer the question.
– Siong Thye Goh
Nov 22 at 13:22

I am not asking anything regarding the test. I am asking you in general what books did you follow for Maths @Siong. I am asking you since you are having high reputation count.
– Akash Roy
Nov 22 at 13:37

|
show 2 more comments

1 Answer
1

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oldest

votes

up vote
3
down vote

From $|f(w)-f(x)| le |w-x|$ we get for $w ne x$:

$|frac{f(w)-f(x)}{w-x}| le 1$. With $w to x$ we see that $|f'(x)| le 1$.

answered Nov 22 at 13:15

Fred

43.6k1644

add a comment |

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

up vote
3
down vote

From $|f(w)-f(x)| le |w-x|$ we get for $w ne x$:

$|frac{f(w)-f(x)}{w-x}| le 1$. With $w to x$ we see that $|f'(x)| le 1$.

answered Nov 22 at 13:15

Fred

43.6k1644

add a comment |

up vote
3
down vote

From $|f(w)-f(x)| le |w-x|$ we get for $w ne x$:

$|frac{f(w)-f(x)}{w-x}| le 1$. With $w to x$ we see that $|f'(x)| le 1$.

answered Nov 22 at 13:15

Fred

43.6k1644

add a comment |

up vote
3
down vote

From $|f(w)-f(x)| le |w-x|$ we get for $w ne x$:

$|frac{f(w)-f(x)}{w-x}| le 1$. With $w to x$ we see that $|f'(x)| le 1$.

answered Nov 22 at 13:15

Fred

43.6k1644

From $|f(w)-f(x)| le |w-x|$ we get for $w ne x$:

$|frac{f(w)-f(x)}{w-x}| le 1$. With $w to x$ we see that $|f'(x)| le 1$.

answered Nov 22 at 13:15

Fred

43.6k1644

answered Nov 22 at 13:15

Fred

43.6k1644

answered Nov 22 at 13:15

Fred

43.6k1644

answered Nov 22 at 13:15

Fred

43.6k1644

add a comment |

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