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.






calculus differential-geometry







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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

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  • 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















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.






calculus differential-geometry







share|cite|improve this 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













up vote
-1
down vote

favorite









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.






calculus differential-geometry







share|cite|improve this question















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




calculus differential-geometry






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edited Nov 22 at 13:21









Gödel

1,393319




1,393319










asked Nov 22 at 13:10









Pauline

11




11




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


















  • 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




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












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




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




@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




@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




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










1 Answer
1






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up vote
3
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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 $|f'(x)| le 1$.






share|cite|improve this answer




























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    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 $|f'(x)| le 1$.






    share|cite|improve this answer

























      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 $|f'(x)| le 1$.






      share|cite|improve this answer























        up vote
        3
        down vote










        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 $|f'(x)| le 1$.






        share|cite|improve this answer












        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 $|f'(x)| le 1$.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 22 at 13:15









        Fred

        43.6k1644




        43.6k1644















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